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Exact Solution of the Dirac Equation with an Equivalent Oscillator Potential

Exact Solution of the Dirac Equation with an Equivalent Oscillator Potential It is shown that a Hamiltonian obtained by adding an energy term λ 2 ρ 2 σ · r K | σ · L + 1 | - 1 to the free-particle Dirac Hamiltonian possesses exact solutions and a discrete spectrum of high degeneracy. In the nonrelativistic limit this leads to an isotropic harmonic oscillator with a spin-orbit coupling term of the Thomas-Frenkel form. The symmetry is likely to be at least as high as S U 3 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review American Physical Society (APS)

Exact Solution of the Dirac Equation with an Equivalent Oscillator Potential

Swamy, N. V
Physical Review , Volume 180 (5) – Apr 25, 1969
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Publisher
American Physical Society (APS)
Copyright
Copyright © 1969 The American Physical Society
ISSN
1536-6065
DOI
10.1103/PhysRev.180.1225
Publisher site
See Article on Publisher Site

Abstract

It is shown that a Hamiltonian obtained by adding an energy term λ 2 ρ 2 σ · r K | σ · L + 1 | - 1 to the free-particle Dirac Hamiltonian possesses exact solutions and a discrete spectrum of high degeneracy. In the nonrelativistic limit this leads to an isotropic harmonic oscillator with a spin-orbit coupling term of the Thomas-Frenkel form. The symmetry is likely to be at least as high as S U 3 .

Journal

Physical Review – American Physical Society (APS)

Published: Apr 25, 1969

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