Physics Seminar

Quantum Harmonic Oscillator in the Fractional State
by Lee Young, Texas Southern University
2011-02-01, 10:00 PM in NSB 156

Abstract

As we show m -wavelets of the SUSY properties in the previous paper, with inspiration of the paper, we show the newly introduced fractional state in the quantum harmonic oscillator. In this fractional harmonic oscillator, using with a tool of fractional calculus, we consider the new type of SUSY structure of generalized harmonic oscillator, which has both positive and negative energy in fractional half integer state. This fractional half integer state can be found when we restore the symmetry in the space for the fermionic space. In the most part, we concentrate on the just have half integer state. This model’s worthiness shows negative energy system similarity of Dirac’s fermionic sea system. This model may influence the whole conventional theory of quantum physics, as well as quantum mechanics and QFT, and even string theory. In this fractional quantum harmonic oscillator model (FQM) can easily expose fermionic state and negative energy level. Conventional SUSY and some quantum mechanics show the fermionic state function and energy is same with bosonic state function except ground. However, our model specifically shows negative state and has two states like spin up and down in the each half fractional state. In this paper we show the entire state of half integer state of harmonic oscillator in the all dimensions. We show the whole hierarchy of state system using raising and lowering operators. The focal points of all physics is symmetry. This half integer state shows the recovery of spontaneously broken symmetry itself in this fermionic state. By comparing with the standard harmonic oscillator, we compare the structure diagram half integer FQM with conventional harmonic oscillator in the SUSY property. In this paper, we construct the FQM and discuss the energy hierarchy system. We analyze these types of solution, which may play a fundamental role in the new SUSY FQM. This model may imply for the improvement of theoretical explanation of Cooper pair (BCS) or BEC theory, and furthermore, this will give strong influence on the theory like QFT, string theory and other condensed matter theory, for even any theory which has based upon the quantum harmonic oscillator. In addition, three-dimensional harmonic oscillator plays a central role in nuclear physics. It provides the underlying structure of the independent-particle shell model and gives rise to the dynamical group structures on which models of nuclear collective motion are based. It features a rich variety of coherent states, including vibrations