On eigenvalue problems in quantum mechanics

Abstract

To solve quantum mechanical eigenvalue problems using the algorithmic methods recently derived by Nikiforov and Uvarov (1988 Special Functions of Mathematical Physics (Basel: Birkhäuser)) and Ciftci et al (2003 J. Phys. A: Math. Gen. 36 11807), one needs to first convert the associated wave equation into hypergeometric or closely related forms. We point out that once such forms are obtained, the eigenvalue problem can be satisfactorily solved by only imposing the condition that the regular infinite series solutions of the equations should become polynomials, and one need not take recourse to the use of the algorithmic methods. We first demonstrate the directness and simplicity of our approach by dealing with a few case studies and then present new results for the Woods-Saxon potential.

Corrected analytical solution of the generalized Woods–Saxon potential for arbitrary $\ell $ states

“…( 3) determined by the NU method is incorrect. If we used any analytical solution methods such as the asymptotic iteration method (AIM) [28], the supersymmetry (SUSY) [12], etc. to solve the corresponding equations with the generalized Woods-Saxon potential, we would find same results in Eq.…”

A comparative interpretation of the thermodynamic functions of a relativistic bound state problem proposed with an attractive or a repulsive surface effect

“…Since then, the Woods-Saxon potential (WSP) energy is used in huge amount of applications in various branches of physics. For instance, in nuclear physics some of recent studies can be given in [3][4][5][6][7][8][9][10][11][12][13][14][15] in addition to two reports [16,17], in atomic and molecular physics [18][19][20][21], in non relativistic [22][23][24][25][26] and in relativistic quantum mechanics [27][28][29][30][31][32][33][34].…”

Comparative Effect of an Addition of a Surface Term to Woods-Saxon Potential on Thermodynamics of a Nucleon

“…The WS potential well [12] is widely employed to model the physical systems in nuclear [12][13][14][15][16][17][18][19][20][21], atom-molecule [21,22], relativistic [23][24][25][26][27][28][29][30][31] and non-relativistic [32][33][34][35][36][37] physics problems.…”