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Neimenggu Shi-da xuebao. Zhexue shehui kexue hanwen ban

A ENTANGLED STATE OF q-DEFORMED HARMONIC OSCILLATOR IN UNIFORM MAGNETIC FIELD

Ruifang Li

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

The degeneration of the energy-level structure of the usual harmonic oscilator in r θ direction in uniform magnetic field is discussed in this article.At the same time,a entangled state is constructed in theory and is verified by Schmidt decomposition.Then,the reduced density matrix and its square are obtained too.It is shown that the reduced density matrix is not equal to its square,the state can be proved to be an entangled state.

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ENTANGLED STATE REPRESENTATIONS FOR DESCRIBING 2-DIMENSIONAL ELECTRON SYSTEM IN UNIFORM MAGNETIC FIELD

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We review how to rely on the quantum entanglement idea of Einstein–Podolsky–Rosen and the developed Dirac's symbolic method to set up two kinds of entangled state representations for describing the motion and states of an electron in uniform magnetic field. The entangled states can be employed for conveniently expressing Landau wave function and Laughlin wave function with a fresh look. We analyze the entanglement involved in electron's coordinates (or momenta) eigenstates, and in the angular momentum-orbit radius entangled state. Various applications of these two representations, such as in developing angular momentum theory, squeezing mechanism, Wigner function and tomography theory for this system are presented. Thus the present review systematically summarizes a distinct approach for tackling this physical system.

International Journal of Modern Physics B•Aug 30, 2004•4 citations
The degeneration of the energy-level structure of the usual harmonic oscilator in r θ direction in uniform magnetic field is discussed in this article.At the same time,a entangled state is constructed in theory and is verified by Schmidt decomposition.Then,the reduced density matrix and its square are obtained too.It is shown that the reduced density matrix is not equal to its square,the state can be proved to be an entangled state.
In the newly constructed entangled state representation embodying quantum entanglement of Einstein, Podolsky and Rosen, the usual wave function of atomic coherent state ∣τ〉 = exp (μJ+-μ*J-)∣j, -j〉 turns out to be just proportional to a single-variable ordinary Hermite polynomial of order 2j, where j is the spin value. We then prove that a two-dimensional time-independent anisotropic harmonic oscillator in a uniform magnetic field possesses energy eigenstates which can be classified as the states ∣τ〉 in terms of the spin values j.
The article studies a simple method for any energy level of three dimensional harmonic oscillator in uniform magnetic field.According to the perturbation theory in degenerate state,wave function of three dimensional harmonic oscillator in the uniform magnetic field,and the popular formula of perturbation matrix elements of three dimensional harmonic oscillator in the uniform magnetic field,the energy levels of first-order for n = 5 are calculated.A formula of energy level for three dimensional harmonic oscillator in the uniform magnetic field is given.
Based on the entangled state representation for describing electron's coordinates under uniform magnetic field, we establish a one-to-one correspondence between quantum Hamiltonian and its classical Weyl function through the introduction of Wigner operator. We also study some new important properties of Wigner function of electron's quantum states, such as its upper bound, and its relation with electron's wave function. These discussions demonstrate the beauty and elegance of the entangled state representation.
We review how to rely on the quantum entanglement idea of Einstein–Podolsky–Rosen and the developed Dirac's symbolic method to set up two kinds of entangled state representations for describing the motion and states of an electron in uniform magnetic field. The entangled states can be employed for conveniently expressing Landau wave function and Laughlin wave function with a fresh look. We analyze the entanglement involved in electron's coordinates (or momenta) eigenstates, and in the angular momentum-orbit radius entangled state. Various applications of these two representations, such as in developing angular momentum theory, squeezing mechanism, Wigner function and tomography theory for this system are presented. Thus the present review systematically summarizes a distinct approach for tackling this physical system.