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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

Quantum equations of motion in the finite-difference approach

A. D. Jannussis

Published Jun 1, 1984• 8 citations
Publisher
DOI
10.1007/bf02751779

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We solve exactly the relativistic finite-difference equation for the quantum three-dimensional ring-shaped Quesne oscillator potential. Our investigation is based on a finite-difference version of relativistic quantum mechanics. So-called relativistic configurational r-space is a key concept here. We show that the radial wavefunctions and angular wavefunctions are expressed through the continuous dual Hahn polynomials and Jacobi polynomials, respectively. A discrete energy spectrum has been found. The radial wave functions and energy spectrum have the correct nonrelativistic limit. We also build a dynamical symmetry group SU (1, 1) for the radial part of the equation of motion, which allows us to find the energy spectrum purely algebraically.