A General Approach for the Exact Solution of the Schrodinger Equation
Cevdet Tezcan, Ramazan Sever
TL;DR
This paper presents a general method for obtaining exact solutions to the Schrödinger equation for certain potentials by transforming it into a second order differential equation and applying the Nikiforov-Uvarov method.
Contribution
It introduces a unified approach to solve the Schrödinger equation exactly for specific potentials using coordinate transformations and the Nikiforov-Uvarov method.
Findings
Exact solutions for well-known potentials are obtained.
Energy eigenvalues and wave functions are explicitly calculated.
The method simplifies solving the Schrödinger equation for certain cases.
Abstract
The Schr\"{o}dinger equation is solved exactly for some well known potentials. Solutions are obtained reducing the Schr\"{o}dinger equation into a second order differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the corresponding wave functions.
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