JOINT MATHEMATICS & PHYSICS COLLOQUIUM

Non-Relativistic Fermionic Quantum Mechanics (Cracking Schrödinger Nutshell)

Young Lee

Department of Physics, Texas Southern University

Young.Lee@tsu.edu

Tuesday, September 25, 2018 2:30 pm – 3:30 pmTexas Southern University Science Building, Room 146

Abstract

The non-relativistic Schrodinger equation was formulated nearly 90 years ago and has been successfully applied to various quantum mechanical systems across multiple scientific fields producing the main developments to quantum theory. The primary importance of Schrodinger’s equation arises in the implementation of the analogue of Newton’s law and continuation of classical mechanics. In the development of relativistic quantum physics, Dirac expanded the theory combining Einstein’s special relativity, quantum mechanics and the so- called fermion particle of half integer spin. This was the first theory to consistently account for special relativity within the context of quantum mechanics. In this paper, we formulate a novel mathematical approach to solve Schrodinger’s equation within the context of particle and wave theory. In our examination, we present a similar, yet unique model of fermion structure, which is consistent with the present day Dirac description. We will introduce and discuss the 1 dimensional structure of a Harmonic oscillator and free particle fermionic state. Additionally, the 3+1 dimensional structure of the fermionic state will be briefly outlined. Finally, we will compare our model with Dirac’s theory for further study. This model is not Lorentz invariant; however, the connection of classical and non-relativistic quantum theory will be explained. We will also talk about the Hydrogen atom within the framework of bound state, fermionic quantum physics.

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Targeted Infusion Grant

TSU was recently awarded a National Science Foundation Targeted Infusion Grant under PI, Dr. Alamelu Sundaresan, with Co-PI Dr. Mark Harvey and CO-Is Drs. John Sapp, Azime Saydam and Bernnell Peltier-Glaze. This project combines structured peer-mentor infused curricula coupled with faculty mentored summer research for the following courses within COSET: MATH 136, CHEM 131, PHYS 237 and BIOL 131. The main objective of the proposal is to increase STEM retention of underrepresented students by offering dedicated peer mentoring and supervised faculty research opportunities. We are excited about this first full-fledged project of its kind at TSU consisting of an active learning concept and associated peer-mentoring, which will benefit both TSU students and the above four departments from June 2017 – May 2020. Peer mentors will be selected from upperclassmen in each of the departments and will be directly supervised by the PI, Co-PI and CO-Is. More to follow…

*Postdoctoral Fellow*– Clark Atlanta University, 2000*Postdoctoral Fellow*– Max Planck Institut Fuer Quantenoptik, 1997*Ph.D. Physics*– University of Pittsburgh, 1996*M.S. Physics*– University of Pittsburgh, 1992*Laurea Physics*– Universitá degli studi di Milano, 1986

Dr. Perotti is currently working in collaboration with Dr. D. Bessis on the development of a new method in the spectral analysis of noisy time-series data for damped oscillators which makes use of J-matrices to evaluate Padé Approximations built on the time-series Z-transform. Applications of the method range from the detection of Gravitational Wave Bursts to the analysis of Magnetic Resonance data.

While in In Atlanta Dr. Perotti perfected codes which -starting from a suitable Pade’ approximant of the desired transmittance- reconstructed, through inverse scattering techniques, the corresponding monodimensional effective self-consistent potential having no bound states. In collaboration with Dr. A. Mezincescu he also wrote codes to calculate and subtract from the potential thus obtained the self-consistent field for a given density of donor dopant ions and finally –trough a change of coordinates- obtain the chemical composition profile (solution of the variable mass BenDaniel and Duke’s equation). The technique allows to efficiently design semiconductor heterostructures given the desired electron reflectance. They furthermore developed codes that, using double Darboux transformations on a given monodimensional potential with one bound state, maximize the asymmetry of the continuum function at a given energy having nonzero dipole matrix element with the bound state. The potential thus obtained optimizes the probability for an electron excited by incident light of a given frequency to be emitted in the desired direction. While In Munich Dr. Perotti developed -for comparison with laboratory experiments- semiclassical and full quantum Monte Carlo simulations of an ion moving in a one-dimensional optical lattice and a weak confining static electric field while at the same time being subject to a periodic driving force. The solution of the Fokker-Planck equation for the system in the diffusion limit, found in collaboration with Dr. V. Alekseev of the Lebedev Physical Institute in Moscow, allows to explain the apparent rise of the spatial diffusion coefficient when increasing the periodic force amplitude. In Pittsburgh Dr. Perotti worked on Classical numerical simulations and calculation of the Lyapunov exponents for a system consisting of an ensemble of (two-level) Rydberg atoms collectively interacting with its own selfconsistent field and an external microwave field in a cavity. By changing the strength of the external field and/or its detuning from the chosen atomic transition, the behavior of the system can be made to change from regular to weakly chaotic and finally to strongly chaotic. The system moreover offers a convenient way to change the total action by varying the number of interacting atoms. It is therefore considered a convenient system to explore the different dependence on the total action of the time at which quantum evolution begins to significantly deviate from the classical one in the case of regular and chaotic systems [G. P. Berman, E. N. Bulgakov and D. D. Holm, Los Alamos Report LA-UR-93_2187 (1993)]. In the first case this time -called “quantum break-time”- is expected to be a polynomial function of the action, in the latter a logarithmic one. His simulations were aimed at identifying the parameter ranges for the different regimes (regular, strongly chaotic, weakly chaotic) and finding their signature in the (averaged) quantities to be measured in the laboratory. He also conducted Classical and quantum simulations of the monodimensional hydrogen atom in a pulsed microwave field and a collinear constant static electric field, both with and without noise. These were compared with experimental results for atoms prepared in extreme Stark states in a static electric field and made to interact with a pulse of microwaves polarized collinear to the static field used to align the atoms. Furthermore he calculated the instantaneous quantum quasienergy (Floquet) levels for the above system and the Husimi functions of the corresponding states and of the projections on those states of the pulsed wavefunction to help interpret the results of the above quantum numerical simulations. In particular he was able to show the relevance of small classical phase space structures to pulsed quantum evolution. In Milano Dr. Perotti helped develop the codes used to numerically investigate the quantum dynamical localization in action (principal quantum number) of the electron probability for a mono (and bi-) dimensional hydrogen atom in a microwave field when the corresponding classical system is chaotic. He has applied similar techniques to the study of the stochastic ionisation of Alkali-metal atoms: microwave experiments with Alkali atoms are easier to perform than with Hydrogen; on the other hand, core effects cause significant deviations from the hydrogenic behaviour. The numerical simulations published by A. Buchleitner and his collaborators are in very good agreement with the laboratory experiment but are very time consuming; moreover only very qualitative arguments and no model has yet been advanced to interpret the regimes where Alkali ionisation deviates from that of Hydrogen. For regime II of A. Buchleitner and coworkers, where quantum effects are still dominant, Dr. Perotti developed an evaluation of the ionisation threshold based on the similarities between the phase space structures of Alkali in monochromatic microwave fields and Hydrogen in a bichromatic field. He has also shown that in the regime of very low microwave frequencies (regime III of A. Buchleitner and coworkers), a classical explanation is possible in terms of Chirikov’s criterion for transition to chaos. Recent research interests of Dr. Perotti also include the quantum double pendulum: a low dimensional autonomous system which in the classical limit displays chaotic behavior . It is simple enough to allow an extensive study which will be able to shed light on more complex chaotic autonomous systems being studied currently: e.g. the Hydrogen atom in crossed static electric and magnetic fields and the Helium atom. He has performed a study of energy curves and compared Husimi functions of eigenstates at important avoided crossings with the corresponding classical surfaces of section. He is now studying the behavior of suitable packets.

- Atomic Physics
- Nonlinear Systems and Chaos
- Advanced Digital Signal Processing

- L.C. Perotti, “Small phase-space structures and their relevance to pulsed quantum evolution: Stepwise ionization of the excited hydrogen atom in a microwave pulse”; Phys Rev. A 81 (2010) 033407 (16pp).
- D. Bessis and L. Perotti “Universal analytic properties of noise: introducing the J-matrix formalism”; J. Phys. A 42 (2009) 365202 (15pp).
- L. C. Perotti, “Ionization of Rydberg alkali-metal atoms in quasistatic electric fields: A classical view of
^{ }the n^{-5 }scaling of the threshold field”; Phys. Rev. A 73, 053405 (2006). - L. C. Perotti, “Proposed Interpretation of Microwave Ionization of Rydberg Alkali-metal Atoms”; Phys. Rev. A 71, 033405 (2005)
- L. C. Perotti, “Quantum double pendulum: Study of an autonomous classically chaotic quantum system”; Phys. Rev. E 70, 066218 (2004).
- Luca Perotti and Daniel Bessis, “Realistic Semiconductor Heterostructures design using Inverse Scattering”; Microelectronics Journal 34 (2003)
- L. Perotti, V. Alekseev and H. Walther; “Transport of a Single Ion in an Optical Lattice: Spatial diffusion and Potential Energy”; Optics Comm. 183 (2000).
- S. Schlipf, H. Katori, L. Perotti, and H. Walther; “Diffusion of a Single Ion in a One-Dimensional Optical Lattice”; Optics Express 3 (1998)
- J.E. Bayfield, S.Y. Luie, L. C. Perotti and M. Skrzypkwosky; “Ionization Steps and phase space metamorphoses in the pulsed microwave ionization of highly excited hydrogen atoms”; Phys. Rev. A 53(1996).
- J.E. Bayfield, S.Y. Luie, L. C. Perotti and M. Skrzypkwosky; “Excited Hydrogen Atoms in Pulsed Microwaves: Journeys to Quantum Chaos and Back”; Physica D 83(1995).
- G. Brivio, G. Casati, I. Guarneri and L. Perotti; “Quantum Suppression of Chaotic Diffusion: Theory and Experiment”, Physica D 33 (1988)

TECH 239

All students pursuing careers in the STEM as well as non-STEM areas must take one of the three service physics courses: Physical Sciences (for non-STEM-majors), College Physics (I & II, consisting of a comprehensive overview of laws of physics, without using calculus), and University Physics (I & II). The latter involves the use of calculus, which is the natural mathematical language of physics.

In addition to the lectures, there are accompanying Labs for College Physics and University Physics. These labs are intended to reinforce basic physics concepts through a “hands-on” approach emphasizing the statistical theory of measurements, and experiencing, first- hand, many of the fundamental laws of Newtonian physics as it impacts mechanics and gravity. These labs introduce students to basic topics such as fluids, waves, and thermodynamics (heat).

- Mechanics and Gravity
- Fluids
- Waves
- Thermodynamics (Heat)

TECH 241

The more advanced Undergraduate Physics lab II introduces students to basic topics such as electricity and magnetism, optics, and modern physics. Students acquire a basic understanding of all these areas through experiments designed to reinforce the lectures. All of these topics are indispensable to the careers pursued by the diverse body of professional interests represented in our students, both majors and non-majors. Students with these skills and knowledge are in high demand in many professions (health sciences, pharmacy, education, engineering, aeronautics, etc.).

These labs are the cornerstone of a student’s immersion into, and understanding of, physics. These Labs will prepare students not only in the technical preparation of physics, but also in the scientific method of empirical research impacting all the sciences. Students will learn team work, sharpen their advanced mathematics skills (i.e. vectors, trigonometry, algebra, and statistical analysis), and develop critical thinking skills based on direct interaction with experiments.

- Electricity and Magnetism
- Optics
- Modern Physics

TECH 246

The Medical and Nuclear Physics Teaching Lab builds upon the successful implementation of a Health Physics program at TSU begun in 2008. Health Physics concerns the understanding of nuclear processes as it affects safe working environments for living organisms (i.e. human beings in particular), within medical facilities, nuclear power plants, food processing centers, etc. Some of the equipment resources in this lab include:

- Alpha Spectrometers
- High Energy Resolution High
- Purity Germanium Detector
- Geiger Mueller Counters
- Lanthanum Bromide Scintillation
- Detector/Multichannel Analyzer
- Wide Energy Neutron Detector
- Survey Meters (Ion Chamber, Geiger Mueller, Neutron Detector)
- Well Detector
- Proportional Counter
- Nuclear Instrumentation Bins and Modules
- Gamma Spectroscopy System

Students enrolled in the traditional health physics program at TSU take several semesters of laboratory classes, which focus on unique hands- on experiments involving various radiation detection apparatuses, analyses, and techniques. In the first laboratory component, students learn how to use a Geiger-Mueller system to measure radiation emitted for various

radionuclide species. In the second installment of the laboratory sequence, students learn how to use a sodium iodide detector system to measure spectroscopic signatures from gamma-emitting radioisotopes. The final course in this sequence is a nuclear electronics laboratory, in which students learn fundamental signal pulse analysis using standard instrumentation commonly employed in nuclear and radiation physics.

Given that Houston hosts the world’s largest Medical Consortium: The Texas Medical Center, it is natural to expand upon the proven Health Physics capabilities into Medical Physics. This concerns the understanding of nuclear physics as applied to medical diagnosis and treatment for illnesses such as cancer. To this extent, the Medical/Health – Nuclear Physics Teaching Laboratory will also expand into this area. TSU- Physics has produced exceptional students that are currently junior radiation officers at the MD Anderson Cancer Center, pursuing advanced degrees at Texas A&M University – College Station, and at the University of Texas at Austin.

Funding provided by grants from the Nuclear Regulatory Commission, NRC-38-07-495.

h3>DEPARTMENT OF PHYSICS

TECH 235

The Medical/Health – Nuclear Physics Laboratory is a research and student research training facility for developing and applying new techniques for effective monitoring of safe radiation levels affecting living organisms in many workplace environments including nuclear power plants, medical diagnostic and treatment facilities, food processing plants, homeland security, etc.

This Laboratory is concerned with basic and applied research in nuclear physics. The “applied” thrust pertains to understanding related issues in the context of medically related, nuclear physics based, diagnostics and therapies impacting diseases; and understanding the radiation thresholds in various workplace settings impacting living organisms and the environment.

Selected students will participate in fundamental research impacting all three areas as specified above. Besides mastering the basic dosimetry and radiation detection skills developed within the curriculum, participating students will apply these skills in the process of basic and applied research. Additional capabilities in Monte Carlo simulation studies in nuclear medicine, etc., will also be developed.

The objective is to develop students that can pursue these studies at a higher level, eventually transitioning into professionals in all the diverse areas where nuclear and radiation safety and treatments are vital. The advanced training received by selected students, developed within the context of performing basic and applied research in medical/health – nuclear physics,

will produce uniquely trained students able to enter the workforce in diverse areas such as nuclear facilities, government laboratories, medical diagnostic and treatment facilities, food processing plants, space exploration, etc. These students may also pursue this advanced training as a stepping stone to careers as oncologists, radiation therapists, etc., within the medical profession.

Houston hosts the world’s largest medical facility, the Texas Medical Center, with tremendous employment opportunities for such students. Some of these students may also elect to pursue Ph. D. in nuclear physics, probing the smallest constituents of matter at the world’s most elite high energy physics facilities. This lab is supported by Nuclear Regulatory Commission grant

NRC-38-10-935.

TECH 232

This is a research and student research training laboratory, emphasizing ongoing departmental research capabilities in noise filtering, atomic physics, and medical physics based research. Students learn modern Nuclear Magnetic Resonance (NMR) techniques which require an understanding of the underlying quantum physics associated with the spinning of atomic nuclei in an ambient, static, magnetic field and the spectrum of the electromagnetic radiation given off by these excitations. NMR is an important physical process with many applications including nuclear waste disposal and cancer detection in soft tissues. In the second case, Magnetic Resonance Imaging (MRI) is the conventional terminology encountered by many in cancer detection protocols. The NMR lab is equipped with the following equipment:

- Earth field Terranova MRI system
- Low field NMR spectrometer
- National Instruments Data Acquisition Instrument

A typical experiment involves probe preparation, field configuration, pulse design, data acquisition and data processing. Students will become familiar with contemporary electronics and digital signal and image processing. Participating students will also learn how to do research as part of a team, each contributing a particular skill. The ultimate objective of the underlying research is to develop more cost effective techniques, requiring low level magnetic fields, for effective cancer detection.

TECH 247

- A Trans-Texas Videoconference Network (TTVN)-system for real-time and recorded course delivery
- Recording facility for most of the courses
- Advanced Smart-Boards to facilitate course delivery

This Laboratory represents a link to the outside world of expanded learning opportunities for our students. Students and faculty members will be able to participate in Distance Learning courses in specialized areas not represented within the Department.

This facility currently supports TSU-Physics’ participation within the Texas Physics Consortium (TPC) which includes eight other campuses across the State, pooling their curriculum resources and expanded faculty specializations (i.e. Astronomy, Cosmology, Geophysics, etc.). The other physics programs participating in the TPC include Midwestern State University, Prairie View A & M University, Texas A&M University-Corpus Christi, Texas A&M University-Kingsville, Tarleton State University, Texas A & M University – Commerce, West Texas A & M University, and Texas A & M University-Central Texas.

Expanding the course offerings available to TSU students will make them more competitive in their post-graduate career objectives. The production of well trained students is essential for sustaining TSU’s research activities. This classroom contributes to the learning process in a very modern way, ensuring the production of the best trained TSU students possible, able to impact ongoing, faculty led, research.

TECH 240

There are key experiments in the history of physics that revolutionized our way of thinking about the fundamental structure of nature and the ensuing laws that characterize physical processes. Some of these experiments can be done by upper level physics majors. These

experiments also serve to expose the student to advanced skills indispensable in today’s advancing

technological evolution impacting many industries. Some of the more traditional experiments include:

**Michelson Morley interferometer** Experiment which confirmed the invariance of the speed of light in a vacuum. This experiment formed the basis for the famous E = mc^{2 }>relation which is at the heart of nuclear fission (i.e. atomic bombs, nuclear power plants, etc.) and nuclear fusion (the energy from the sun, and potentially future energy machines which produce less radioactive bi-products tha

n conventional nuclear power plants).

**Millikan Oil Drop Experiment** – that measured the charge on an electron.

**X-Ray Diffraction** for discovering the crystal structure of compounds.

**Davisson Germer Experimen**t which revealed the duality principle of matter (i.e. what we call a particle can sometimes behave as a wave) – “matter waves.”

**Nuclear Magnetic Resonance** – atomic nuclei, when placed in magnetic fields, will occupy different energy levels that can be excited and de-excited through electromagnetic radiation. This is relevant in many fields, particularly medicine. Other important experiments impact nuclear physics, laser physics, semiconductors, superconductivity, nanostructures, etc. These labs are the cornerstone of a student’s immersion into, and understanding of, physics. Physics lab courses are the stepping stones into student’s participation in faculty led research. This Lab ensures the production of high caliber students able to assist faculty in their research efforts.

Click here to view the press release.

*ITAMP Fellow:*Harvard-Smithsonian Center for Astrophysics*PhD in Physics:*Georgia Institute of Technology*MS in Physics:*Bucharest University

Dr. Vrinceanu was born and raised in Romania. As a student at the “Mihai Viteazul” High School in Ploiesti, he was awarded the bronze medal at the *International Physics Olympiad* held in London. This scientific competition is the equivalent of the Olympic Games for sports and considers the very best students that represent their own countries. Immediately after obtaining his University degree in Mathematical Physics, he was offered the position of Assistant Professor in the Department of Theoretical Physics at the Bucharest University.

He obtained his doctoral degree in Theoretical Atomic Physics from Georgia Institute of Technology in Atlanta. The problem treated in his PhD Thesis made a signi!cant theoretical contribution providing an elegant and efficient solution to an outstanding problem incapable of being solved for more than 40 years. In recognition, he was awarded the Sigma-Xi award of *Best Ph.D Thesis 2001* and he was selected for *Thesis Prize* of the American Physical Society of Division of Atomic, Molecular and Optical Physics (DAMOP).

At the Institute for Theoretical Atomic and Molecular Physics at the Harvard-Smithsonian Center for Astrophysics Dr. Vrinceanu was the leader in a theoretical investigation of strongly magnetized antihydrogen atoms, aimed to clarify understanding and interpretation of the recent experiments at the European Center for Nuclear Reseach (CERN) by Harvard scientists. Their results on formation and electric !eld ionization of highly excited *anti-hydrogen atoms* are ground breaking and completely changed the way the experimental data is analyzed. For the upmost importance of the research, their work published in Physical Review Letter was featured on the journal cover.

Dr. Vrinceanu was granted the prestigious Director Fellowship at Los Alamos National Laboratory where he worked on large scale Monte Carlo and Molecular Dynamics Simulations of cold magnetized and un-magnetized plasmas.

**Theoretical studies** of:

- matter at extreme conditions: novel computational algorithms for ultracold ionized gases, ultrafast pulses, quantum computing and BEC
- formation, capture and detection of anti-hydrogen atoms in a Penning trap
- interaction and collisions in ultracold Rydberg gases and frozen plasmas, electron impact ionization of Rydberg atoms, interaction between Rydberg atoms, radiative processes involving Rydberg atoms, three-body recombination
- collisional and radiative properties of metastable helium atoms, collisional broadening and shift of atomic and ionic lines

- T. K. Langin, T. Strickler, N. Maksimovic, P. McQuillen, T. Pohl,
*D. Vrinceanu*, and T. C. Killian, “Demonstrating universal scaling for dynamics of Yukawa one-component plasmas after an interaction quench”, Phys. Rev. E*93*, 023201 (2016) - C. R. Handy,
*D. Vrinceanu*, C. B. Marth and H. A. Brooks, “Pointwise reconstruction of wave functions from their moments through weighted polynomial expansions: an alternative global-local quantization procedure”, Mathematics*3*, 1045 (2015) - C. R. Handy and
*D. Vrinceanu*, “Orthogonal polynomial projection quantization: a new Hill determinant method”, J. Phys. A*46*, 135202 (2013) *D. Vrinceanu*, R. Onofrio and H. R. Sadeghpour, “Angular momentum changing transitions in proton-Rydberg hydrogen atom collisions”, Astrophysical Journal*747*, 56 (2012)

- National Science Foundation : $991,206, duration 2014-2017 as Co-Pi, Research Infrastructure for Science and Engineering: “Characterization of Biomolecular Response to Environmental Stress”
- Army Research Office : $634,220, duration 2013-2016 as Co-Pi. Research and Education Program for HBCU: “Many Body Density Matrix Theory: Excitations and Time Dependent Response”
- National Science Foundation : $4,887,000, duration 2011-2016 as Co-I, Centers of Research Excellence in Science and Technology: “Center for Research on Complex Networks”
- National Science Foundation : $220,000, duration 2011-2013 as Co-Pi, Major Research Instrumentation: “Acquisition of HPC at Texas Southern University to Expand Capabilities for Research and Training through Shared High Performance Computing”
- Seed Grant, Texas Southern University, “Decoherence Related Challeges in Quantum Computing”, 2009 ($15,000)

- Ph.D., Astrophysics & Astronomy, University of Pennsylvania, Philadelphia, PA. September/1982-March/1989. Thesis title:”A Three-year Study of the OH Masers in Orion-KL and its correlation with the Ammonia emission”, Supervisor: Ken Johnston (Naval Research Laboratories).
- M.S., in Astronomy, University of Pennsylvania, Philadelphia, PA. May/1988.
- B.S., Physics, University of Puerto Rico, Rio Piedras, P.R., Cum Laude Honor Graduate. August/1977 to May/1981.

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• CONACyT PDRA-Fellowship for Mexican Young Researcher #250356 : US$50,000.0, 2015-2017

• Western Alliance to Expand Student opportunities – US$2,378.0, 2014

• Graduate Studies, Brigham Young University – US$90,000.0 for 3 years to support a

graduate student, 2012

• Western Alliance to Expand Student opportunities – US$2,256.0, 2012

• Western Alliance to Expand Student opportunities – US$10,630.0, 2011

• Federal Government Grant – Ecology Institute of Gto, US$170,000.0, 2010

• Guanajuato State Government Funding, US$350,000.0, 2008-2010

- PhD in Theoretical Physics, University of Houston, Houston, 2005 Dissertation : Minimum Uncertainity Wavelets in SUSY Quantum Mechanics , the Theory of Coherent States, the Theory of Strings, and the Fermionic Harmonic Oscillator.
- DMin in Practical Theology, Houston Graduate School of Theology, Houston, 2001 Dissertation: An Approach to the Paradigms of Spiritual Leadership for Creative and Effective Ministry.

Young Lee was born in South Korea. He studied theoretical physics at the Yonsei University where he obtained his B.S. and M.S. in 1981 and at University of Houston where he obtained his Ph.D. in 2005. He was Research Assistant at the same university (2005-2006). Since 2007, he is now serving as a Visiting Professor at the Texas Southern University. Also, he was also conferred doctoral degree (D. Min) in the field of practical theology from Houston Graduate School of Theology in 2001. He has been served as an ordained minister in Christian church for many years before he joins the physics faculty of TSU.

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His research fields are theoretical physics in quantum fields and computational physics in statistical mechanics (condensed matter physics). In theoretical physics part, his major interests are concentrating on the foundation of quantum mechanics, quantum field theory, string theory, and black holes theory. He utilizes the minimum uncertainty wavelet model and harmonic oscillator model as implementations to explore them. Using the minimum uncertainty wavelet model which is the minimization solution of Heisenberg uncertainty, He explores the SUSY quantum mechanics, and coherent theory and string theory. In these theories, He is looking for a simple model to compare how different and similar with the traditional quantum physics.

He is also interested in medical physics which is applied of physics tomedicine. It generally concerns physics as applied to medical imaging and radiation therapy. He has a plan to introduce medical physics programming to TSU in near future. He has currently been trainned in M. D. Anderson Cancer Center.

Another present research interest is to develop the virtual laboratory in physics education. We call this virtual laboratory as Virtual Reality Laboratory for the Experimental Mathematical Modeling o Physical Systems (ViRLEMPS). This lab mainly focus on the science related students and this provide them with understanding easily the sophisticate physical phenomena and this method enable to grasp the conception of difficult mathematically formalized natural phenomena.

For the part of the computational physics, non-equilibrium statistical physics and econophysics are my present concerns to research, which aims to find the simple model and apply to the essence of experimental phenomena. These works involve the computer simulations. The followings are descriptions of the major on-going project of his research.

Minimum Uncertainty Wavelets: I explore the SUSY properties and string aspects through the recently derived constrained minimum Heisenberg uncertainty m-wavelets. The several types of raising and lowering operators play a fundamental role in the SUSY structure of these wavelets. Compared with the harmonic oscillator, the m-wavelets naturally manifest the SUSY properties. Using the results, he construct a supercoherent theory of these wavelets. In addition, the m-wavelets and harmonic oscillator belong to different classes in string theory. The results should be of interest for the supersymmetric theory of quantum fields and string theory. He derives isotropic non-Cartesian multi-dimensional solutions using the three different methods; the solution of differential equations, Fourier transformation, and the creation and annihilation operators. He derive multi-dimensional ALDAF (Associate Laguerre Distributed Approximating Functionals) which is a collection of m-wavelets. ALDAF and its non-Cartesian solutions are good approximation tools for physics and other sciences. In the application to string theory, his model is more efficient for compactification of the extra-dimension because of lower uncertainty when his model is compared with harmonic oscillator. He is preparing m-wavelet relativistic quantum mechanics and m-wavelet quantum field theory.

Fermionic Harmonic Oscillator: He explore two kinds of model which are the general superpotential model and the fractional (half-integer) harmonic oscillator. In my general superpotential model, fermionic solutions of the harmonic oscillator are generated in terms of the well-behaved Hermitian polynomial solutions. The half-integer harmonic oscillatior model shows the natural SUSY property and its solutions are generated in terms of the parabolic cylinder functions. For the case of the general superpotential model, as same as the conventional SUSY quantum mechanics, the symmetry of the fermionic state is always opposite from the symmetry of the bosonic state. Thus, if for any state the boson has symmetric function, then the fermionic state is an anti-symmetric function and vice versa. However, for the case of the fractional (half-integer) harmonic oscillator, this is only true for the broken SUSY. In the case of unbroken fractional harmonic oscillator SUSY, both bosonic and fermionic state has same symmetry function. The multi-dimensional versions of these models are considering and supercoherent theorys of the fractional harmonic oscillator is an interesting project now.

Non-Equilibrium Statistical Physics: Self-organized networks of competing Boolean model is considered. A model of Boolean agents competing in biology, ecosystems, social sciences, and economy is considered where each agent bases his action on information obtained from a small group of other agents. The agents play a competitive game that rewards those in the minority. After a long time interval, the poorest players strategy id changed randomly, and the process is repeated. Eventually the network evolves to a stationary but intermittent state where random mutation of the worst strategy can change the behavior of the entire network, often causing a switch in the dynamics between attractors of vastly different lengths. Development of canalization leads to a reduction in the variation of phenotype expression relative to the complexity of the genome has long been thought to be an important property of evolving biological systems. We show that a highly canalized state develops in the process of self-organization recently discovered in N-K Boolean networks that evolve based on a competition networks in developmental systems. Unlike other proposed evolutionary mechanism that select for canalization, this mechanism does so while maintain the systems capacity for further evolution in the steady state.

Econophysics: He utilizes two kinds of approach which are the non-Gaussian distribution of return method and self-organization model in agent network method. Analytical interpretation for the distribution of returns is expressed in terms of the diffusion rate when the consensus value is assumed to be fixed in time. The range of the behaviors observed with a simple model covers the range of non-Gaussian behaviors seen in the distribution of returns of real financial market. Also, He explores that the development of self-organization in agent-based network models of economic markets. Although individual traders in a market obey simple rules, the way that they interact and exchange information can lead to the market self-organizing into a complex state. The overall performance of the market can be affected by the self-organization of the traders. We are trying to understand the process of self-organization in markets, and how to optimize the process to maximum advantage.

ViRLEMPS: The virtual reality environments in science and engineering is just to utilize the computer as experimental laboratory and it shows and can understand the real, physical, and the three dimensional phenomena in nature. He especially focus on 3D simulation analysis will help students to understand in physics area, for example, mechanic, electromagnetism, quantum mechanic, solid state physics, and other physics field.

Other related topics: In addition to the above mentioned subjects, He also have been interesting the fractional calculus in physics application. Especially, fractional diffusion problem , fractional harmonic oscillator, and fractional Quantum Hall effect are among these interests. In the flexural oscillations of an elastic beam will be interesting to solve with fractional Laplacian. In addition, He is interested in the black holes thermodynamic theory from near horizon. PT symmetric quantum mechanics is another interesting subject. He is now trying to get the exact wave function solution of Bender and Boettecher potential.

- Kouri, D.J.; Papadakis, M., Kakadiaris, I.; Hoffman, D., J. Phys. Chem. A 107, 7318, 2003.
- Hoffman, D. K.; Kouri, D.J., Phys. Rev. A 65, 052106-1, 2002.
- Hoffman, D. K.; Kouri, D.J., Phys. Rev. Lett. 85, 5263, 2000.
- Hoffman, D. K.; Kouri, D.J., Phys. Chem. 97, 2907, 1993.
- Lee, Y., Kouri, D.J. , Hoffman, D. K.; Minimum Uncertainty Wavelets in SUSY Quantum Mechanics, The Theory of Coherent States, and String Theory, in preprint, 2005

*Bachelor of Science in Physics*, Cum Laude Virginia State University, Petersburg, Virginia, May 1992*Master of Science in Physics*Hampton University, Hampton, Virginia, May 1995*Doctor of Philosophy in Experimental Nuclear Physics*Hampton University, Hampton, Virginia, May 2001

Dr. Harveys doctoral research experiment in medium energy nuclear physics was carried out at the National Institute for Nuclear and High Energy Physics in Amsterdam, The Netherlands. While a doctoral candidate at Hampton University, he developed several detailed Monte Carlo simulation codes to model his Ph.D. experiment. Dr. Harveys other research tasks included operating the data acquisition system for the beam, target, and detector systems as well as data analysis. After completing his doctoral work, Dr. Harvey went on to become a postdoctoral research assistant in the PHENIX collaboration at the Brookhaven National Laboratory (Upton, NY) where he collaborated on research in the field of relativistic heavy ion collision physics. His duties included data analysis, programming, and electronic testing and installation of front-end electronic modules used for one of the detectors (Time Expansion Chamber) in the PHENIX experiment. After completing his postdoctoral tenure at Brookhaven, Dr. Harvey accepted a visiting assistant professorship at the Rochester Institute of Technology (Rochester, NY) where he taught introductory physics courses for one year, he then returned to research, accepting a postdoctoral fellowship at the University of Texas M. D. Anderson Cancer Center (Houston, TX). The National Institutes of Health awarded him a Ruth L. Kirschstein National Research Award grant during his fellowship in the radiation physics department for work related to secondary neutron exposure in proton radiotherapy. He used the MCNPX Monte Carlo simulation code to model both the therapeutic absorbed dose and secondary neutrons from the passive scattering treatment nozzle at the Proton Therapy Center. Dr. Harvey is currently a visiting assistant professor of physics at Texas Southern University in Houston, Texas.

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NIH F32 (PI)