JOINT MATHEMATICS & PHYSICS COLLOQUIUM
Non-Relativistic Fermionic Quantum Mechanics (Cracking Schrödinger Nutshell)
Department of Physics, Texas Southern University
Tuesday, September 25, 2018 2:30 pm – 3:30 pmTexas Southern University Science Building, Room 146
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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The department of Mathematics at the Texas Southern University will hold a conference on 9/22/2018-9/23/2018 with a tentative title ‘Invitation to Mathematics’
Goals of the conference are:
Mathematics Department Seminar: Careers in Biostatistics by Dr, Lem Moye, University of Texas Health Science Center at Houston. 3-4 pm Nov. 2, SB 153. Click here to view pdf more.
Mathematics Department Colloquium: Inverse Problems and Applications. Dr Tuncay Aksotum, University of Texas at Arlington.
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Dr. Williams was born in Greenwood, MS.
Texas Southern University College of Science, Engineering and Technology Distinguished
Partial Differential Equations, Applied Mathematics, & Difference Equations
Teaching College Algebra, Business Calculus with Applications,
Trigonometry, PreCalculus, Mathematics for Elementary School Teachers,
Calculus, Number Theory
Teaching to use Calculators: T1-83 , TI-92
Teaching to use Mathematical Softwares: Maple, Derive, MS Excel
Prepare Secondary Mathematics Pre-Excel Exams
A member of Department Core Curriculum committee
Memberships in Professional Organizations:
Mathematical Association of America
National Council of Teachers of Mathematics
Parametric Equations Describe Curves, April 20001, Vision – Potential
Watering Horses, January, 1997, Vision – Potential
My research is in the area of nonlinear dynamical systems with focuses on theory on dynamics of networks of differential equations and its applications. Currently, I work on
NSF – Research Initiation Award: Studying the Dynamics of Network Systems by Using
Ordinary Differential Equations and Boolean Frameworks ($283,194). 5/1/2018 – 4/30/2021, PI
Seeds Grant at Texas Southern University ($8,000), 2015.
L. Huang, D. Vrinceanu, Y. Wang, N. Kulathunga and N. Ranasinghe. Discovering Nonlinear Dynamics Through Scientific Machine Learning, IntelliSys 2021 proceedings.
N. Kulathunga, N. Ranasinghe, K. Kingsman, D. Vrinceanu, L. Huang, and Y. Wang. Effects of Nonlinearity and Network Architecture on the Performance of Supervised Neural Networks, Algorithms 2021, 14, 51. https://doi.org/10.3390/a14020051.
Y. Wang, Z. Kilpatrick and K. Josic. A hierarchical model of perceptual multistability involving interocular grouping. Journal of computational Neuroscience. 2020. (DOI: 10.1007/s10827-020-00743-8)
M. Golubitsky, Y. Zhao, Y. Wang and Z. Lu. The Symmetry of Generalized Rivalry Network Models Determines Patterns of Interocular Grouping in Four-Location Binocular Rivalry, J. Neurophysiology. Sept. 18, 2019 (doi:10.1151/jn.00438.2019).
A. Ben-Tal, Y. Wang, and M. C. Leite. The logic behind neural control of breathing pattern. Scientific Reports 9: 9078, 2019. (doi.org/10.1038/s41598-019-45011-7)
Y. Wang, K. Chilakamarri, D. Kazakos and M. C. Leite. Relations between dynamics of network systems and their subnetwork systems.AIMS Mathematics, 2(3): 437-450, 2017
Y. Wang, B. Omidiran, F. Kigwe and K. Chilakamarri. Relations between the conditions of admitting cycles in Boolean and ODE network systems, Involve, Vol.10, No.5, (2017),813. DOI 10.2140/involve.2017.10.813 (B. Omidiran and F. Kigwe were two undergraduates).
A. Jacot-Guillarmod, Y. Wang, C. Pedroza, H. Ogmen, Z. Kilpatrick, K. Josic. Extending Levelt’s Propositions to perceptual multistability involving interocular grouping. Vision Research. Volume 133, April 2017, Pages 37-46.
C. Diekman, M. Golubitsky and Y. Wang. Derived Patterns in Binocular Rivalry Networks. J. Math. Neuro. (2013)
C. Diekman, M. Golubitsky, T. McMillen and Y. Wang. Reduction and dynamics of a generalized network with two learned patterns. SIAM J. Appl. Dynam. Sys.11 (4) (2012) 1270-1309.
M. Golubitsky, D. Romano, and Y. Wang. Network Periodic Solution: Rigid phase shift. Nonlinearity. 25 (2012) 1045-1074.
Y. Wang, P.Paszek, C. A. Horton, H. Yue, M. R.White, D.B. Kell, M. R. Muldoon and D.S. Broomhead. A systematic study of the response of a NF-kappaB signalling pathway to TNFalpha stimulation. 297 (2012) 137-147. Journal of Theoretical Biology
Y. Wang, P. Paszek, C. A. Horton, D. B. Kell and M. R. White, D. S. Broomhead and M. R. Muldoon. Interactions among oscillatory pathways in NF-kappaB signalling. 5(23), 2011.BMC Systems Biology
Structure of the Solution Space of Certain Linear Equations, JDE 59(1985), 229 242 (with G.J. Etgen and G.D. Jones)
On the Factorization of Ordinary Linear Differential Operations, TAMS 297(1986), 717 728 (with G.J. Etgen and G.D. Jones)
Asymptotic Behavior of Solutions of a Third Order Difference Equation Portgualiae Mathematica 44(1987), 113 117 (with B. Smith)
Fourth Order Difference Equations: Oscillation and Nonoscillation, Rocky Mountain Journal of Mathematics 23(1993), 781 795
Oscillation Properties of Nonlinear Difference Equation, Portugaliae Mathematica 52(1995), 15 24 (with M. Sun)
Azime Serpil Saydam, TSU Associate Professor and Department Chair of Mathematics, began working at TSU in January 2011. She earned a Ph.D. in mathematics from the University of Nebraska at Lincoln. Her research areas are commutative algebra, algebraic geometry, commutative rings, and computational algebra. She had been Assistant Professor, tenured Associate Professor, Assistant Department Head, and Department Head of Mathematics and Physics at University of Louisiana at Monroe for 11 years.
Field 1, Field 2, Field 3
B. Wilson, V. Obot, and W. E. Taylor, (2009), “A Model for Improving Graduation and Retention Rates for STEM Students at an HBCU” in Models for Success, 3rd Edition (Published by TMCF 2009)
R.Weinstein, R.P Sawh, J. Liu, D. Parks, V. Obot and H. Weber, “Threshold for creation of ionazation pinning centers in YBCO by heavy ions,” Physica C:357-360 (2001) 743-746
R. Sawh, R.Weinstein, Y. Ren, V. Obot, and H. Weber “Uranium fission fragment pinning and centers in melt textured YBCO,””Physica C: 341-348(2000) 2441-2442
V. Obot, R. Weinstein, Y. Ren, J. Liu, R. Sawh and G. Johnson,”Development and Fabrication of High T Trapped Fields Magnents” Jour. National Tech. Assoc., 69(3) 17, (1995)
Y. Ren, J. Liu, R. Weinstein, V. Obot, and C. Foster, “Quasi permantent superconducting magnet of very high feild”, J. Appl. Phys. 73(10),6533,(1993)
“Radiation Interuniversity Science and Engineering Program” $75,000. National Aeronautics and Space Administration (NASA). (6/1/2007 – 5/31/2008)
“Science and Technology Enhancment Program (STEP)’. $2,500,000 National Science Foundation (NSF) (9/1/2006 – 8/31/2011) Co-PI with Bobby Wilson as PI.
“Radiation Interuniversity Science and Engineering Program” $37,500. National Aeronautics and Space Administration (NASA). (6/1/2006 – 5/31/2007)
“Magnetic separation of erythocytes from human blood.” $23,809. TSU seed grant(2002).
“R and D on Accelerators” $19,000. TNRLC (1992)
Non-oscillatory Solution Types for m-th Order Difference Equation, Discrete Week organized by the Texas Southern Department of Mathematics, February 1986
Inverses in Mathematics, Texas Southern Student Chapter of the National Association of Mathematicians (NAM), April 2002
Self Invertible Elements in n Z , National Association of Mathematicians (NAM), 2004 Regional Conference, March 2004
Self Invertible Elements in n Z , Texas Southern University Workshop on Mathematical Awareness, April 2004
Funded Research Grants:
Principal Investigator: Robert M. Nehs
Development of a New Finite Element Grid for Limited Area Weather Models
US Air Force Office of Scientific Research
January, 1987 August, 1987 $20,000