Approximate solutions of the Schrödinger equation with the generalized Morse potential model including the centrifugal term

Abstract

By using a new improved approximation scheme to deal with the centrifugal term, we solve approximately the Schrö dinger equation with the generalized Morse potentials for the arbitrary angular momentum values. The bound state energy spectra and the unnormalized radial wave functions have been approximately obtained by using the basic concept of the supersymmetric shape invariance formalism and the function analysis method. The numerical experiments show that our approximate results are in better agreement with those obtained by using the numerical integration approach than the approximate results obtained by using the conventional approximation scheme to deal with the centrifugal term. We also calculate the rotational transition frequencies for HF molecule and compare them with the experimental data.

Application of the Nikiforov-Uvarov Method in Quantum Mechanics

“…The derivative of this energy expression according to n gives an idea about the maximum vibrational quantum number so that the result is n max = β/2 √ γ − 1/2 (Berkdemir & Sever, 2009;Zhang et al, 2011). Let us now find the corresponding wavefunction of the Morse potential.…”

Eigensolutions of the Schrödinger equation with a class of Yukawa potentials via supersymmetric approach

“…As a result, many authors have solved both relativistic and non-relativistic wave equations with these potentials. For instance, Zhang et al [2] obtained approximate solutions of the Schrödinger equation with the Generalized Morse potential model including a centrifugal term. Jia et al [3] solved sixparameter exponential-type potentials.…”

Approximate Analytical Solutions of the Effective Mass Klein-Gordon Equation for Two Interacting Potentials

“…When a quantum system is in strong potential field, the relativistic effect is usually been taken into consideration which gives the correctness for the nonrelativistic quantum mechanical system 2 . It is well known that the solutions of these equations play an essential role in the relativistic regime for some physical potential model such as Yukawa potential 3 , Deng-Fan potential 4 which can easily be transformed into other useful potential like Tietz potential and Morse potential 5,6 . The relativistic effects describe a …”