Abstract
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.
Highlights
Since the advent of quantum mechanics, several methods have been developed in order to find the exact energy spectrum of bound states in stationary quantum systems
Hartmann potential introduced by Hartmann is one of the noncentral potentials, which can be realized by adding a potential proportional to Coulomb potential [11,12,13,14,15,16]
The relativistic linear interaction, which is called the relativistic oscillator due to the similarity with the nonrelativistic harmonic oscillator, has been subject of many successful theoretical studies. Such a space has interesting property and algebra; for example, there are some articles in which a free particle has been studied in different situations; Dirac oscillator system that is initiated by a relativistic fermion is subjected to linear vector potential [23,24,25]
Summary
Since the advent of quantum mechanics, several methods have been developed in order to find the exact energy spectrum of bound states in stationary quantum systems. Since Hartmann and Ring-Shaped Oscillator Potentials contained two radial and angular parts, the secondorder differential equation is considered in the spherical polar coordinates. In the radial part of differential equation, the relativistic energy spectrum can be gotten by comparison with the nonrelativistic solvable Schrodinger equation In this comparison, the relativistic energy spectrum is obtained based on the nonrelativistic energy spectrum and the wave function of the nonrelativistic space will be considered for calculation of the relations between nonrelativistic and relativistic parameters. (10) can be separated to three differential equations in the three dimensions φ, r, and θ:
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
