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Yunnan Daxue xuebao. Shehui kexue ban

The eigenvalues of the orbit angular momentum in noncommutative phase-space

Zhengren Zhang

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

In order to discuss the orbit angular momentum of the charged particle in noncommutative phase-space,the coordinate operators can be transformed into the annihilation and creation operators through a transformation matrix firstly.And then obtain the corresponding eigenvalues with the method of diagonalization.The result shows that there exists the zero-point angular momentum which is affected by the noncommutative parameters.

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In order to discuss the orbit angular momentum of the charged particle in noncommutative phase-space,the coordinate operators can be transformed into the annihilation and creation operators through a transformation matrix firstly.And then obtain the corresponding eigenvalues with the method of diagonalization.The result shows that there exists the zero-point angular momentum which is affected by the noncommutative parameters.
In noncommutative spaces to maintain Bose–Einstein statistics for identical particles at the non-perturbation level described by deformed annihilation-creation operators when the state vector space of identical bosons is constructed by generalizing one-particle quantum mechanics it is explored that the consistent ansatz of commutation relations of phase space variables should simultaneously include space–space non-commutativity and momentum–momentum non-commutativity, and a new type of boson commutation relations at the deformed level is obtained. Consistent perturbation expansions of deformed annihilation-creation operators are obtained. The influence of the new boson commutation relations on dynamics is discussed. The non-perturbation and perturbation property of the orbital angular momentum of two-dimensional system are investigated. Its spectrum possesses fractional eigen values and fractional intervals.
Abstract The charged particle confined by a harmonic potential in a noncommutative planar phase space interacting with a homogeneous dynamical magnetic field and Aharonov-Bohm potentials is studied. We find that the canonical orbital angular momenta of the reduced models, which are obtained by setting the mass and a dimensionless parameter to zero, take fractional values. These fractional angular momenta are not only determined by the flux inside the thin long solenoid but also affected by the noncommutativities of phase space.
Abstract In this chapter we introduce the concept of orbital angular momentum into the mathematical language of quantum mechanics. We discuss the commutation relations of the corresponding operators and their roles as generators of rotations in the context of the theory of Lie groups and Lie algebras, focusing on the three-dimensional rotation group SO(3). We further examine how scalar and vector-valued operators transform under spatial rotations. We then turn to the derivation of the eigenfunctions and eigenvalues of the angular-momentum operators, for which we follow a dual approach in analogy to that employed for the harmonic oscillator in Chapter 5. Using both the algebraic ladder-operator method and an analytical method using spherical polar coordinates we discover the relevant azimuthal and magnetic quantum numbers and their relation to the spherical harmonics and the Legendre polynomials
Discusses angular momentum,an important but seemingly difficult concept in physics.An analysis of angular momentum direction in fix axis movement finds the direction different from the fix axis in normal condition while a probe into the angular momentum in atom movement leads to the conclusion that the atomic orbit angular momentum operator are not complete set of mechanical eigenvalues and eigenvectors and the orbit angular momentum operator is non-observable.Points out a quantum physical nature in photon spin angular momentum,which is not corresponding to classical physics.