The series solutions of the non-relativistic equation with the Morse potential

Yu Jiang, Shi‐Hai Dong, Guo-Hua Sun

Luis A. Poveda, Bill Poirier, Arthur R. B. de Magalhães

Quantum relativistic solutions for a particle in a one-dimensional Morse potential are presented using methods previously proposed and applied to a particle in a harmonic oscillator. The methods lead to both numerical and analytical solutions, with the latter allowing smooth variation of the system parameters from non-relativistic to ultrarelativistic limits. Analytical expressions for the energy levels and wavefunctions are obtained, as solutions to a Schrödinger-type equation, including relativistic effects through a state dependent rescaled mass. The eigenstates of the Morse potential exhibit suitable and smooth behavior, and approach the corresponding harmonic oscillator solutions as the depth of the Morse potential well increases, as expected. A comparison is also presented between the relativistic harmonic oscillator obtained with this method, and the so-called Klein-Gordon oscillator.

C. A. Onate, J. O. A. Idiodi

Using the supersymmetric quantum mechanics (SUSY) approach, we obtained analytical approximate solutions to the Dirac equation with an improved Tietz diatomic potential function under spin and pseudospin symmetries. The energy eigenvalues equation and the corresponding wave spinor for the two symmetries have been explicitly obtained. The non relativistic limit of the spin symmetry has been obtained. The solution of Morse, Deng-Fan, and Rosen-Morse were obtained by changing the numerical value of q We have also obtained the thermodynamic properties of a system under the improved Tietz potential function.

Ph. Gueret, Jean Pierre Vigier

Sami Ortakaya

The approximate analytical solutions of the Klein—Gordon equation with equal scalar and vector q-deformed Morse potential are presented for arbitrary ℓ-states by using Laplace integral transform. The energy eigenvalues and corresponding wave functions are obtained for n and ℓ values. In this study, in the non-relativistic limit c → ∞ , it has been also provided that the energy eigenfunctions for Klein—Gordon system turn into those for Schrödinger one.