An approach to the solution of Schrödinger's equation

Boris V. Alekseev, A. I. Аbakumov

Anirban Bose

A method has been introduced to derive the solution of the time-independent Schrodinger equation for the simple harmonic oscillator. A trial solution has been chosen as the product of the divergent part of the approximate asymptomatic solution of the Schrodinger equation and an unknown function. By inserting this trial solution into the same equation, an equation of that unknown function is obtained. This equation has a recursive property which has been exploited to obtain the solutions of the equation. It is all about reconstruction of the equation with different solutions of that unknown function by repetitive differentiation and that ultimately leads to the wave functions of the Schrodinger equation for harmonic oscillator.

M. Roncadelli

Mohammad Solimannejad, S. K. Moayedi, Majid Tavakoli

Abstract In this article, we discuss the relationship between exact solvability of the position‐dependent mass Schrödinger equation with analytical solutions of an ordinary Schrödinger equation in quantum mechanics. Furthermore, it is demonstrated that nonperturbative solutions of ordinary Schrödinger equation for a sextic potential leads to a large class of exact solutions for the position‐dependent mass Schrödinger equation. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

G. F. Torres del Castillo

We present two examples where the Schrödinger equation admits R-separable solutions. In one of them (a particle in a uniform force field) the Schrödinger equation admits separable and R-separable solutions.

Galina A. Nemova