Generation of exactly solvable ring shaped potentials of non relativistic quantum mechanics

陈昌远, 陆法林, 孙东升 +1 more

Vladislav G. Bagrov, Dmitriy M. Gitman

A. A. Suzko

Arup Bharali

We apply the extended transformation method, comprising a coordinate transformation supplemented by a functional transformation, to generate (regenerate) exactly solvable ring-shaped potentials from already known exactly solvable central potentials for physical quantum systems in a non-relativistic regime. The angular wave functions corresponding to the generated potentials are transformed from the radial wave functions of the original central potentials in a very straightforward way and they are also shown to be normalizable.

Sh. M. Nagiyev, Narmin Nasibova, V. A. Tarverdiyeva +1 more

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.

Zahra Bakhshi

The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrödinger-like equation obtained by Dirac equation with the nonrelativistic solvable models is the most efficient method. By this technique, the exact relativistic solutions of Dirac equation for Hartmann and Ring-Shaped Oscillator Potentials are accessible, when the scalar potential is equal to the vector potential. Using solvable nonrelativistic quantum mechanics systems as a basic model and considering the physical conditions provide the changes in the restrictions of relativistic parameters based on the nonrelativistic definitions of parameters.