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Chinese Physics C

Solution of the Schrödinger equation for a particular form of Morse potential using the Laplace transform

M. Zarezadeh, Mohammad Kazem Tavassoly

Published Apr 1, 2013• 12 citations
Publisher

Abstract

In this paper, we have solved the Schrödinger equation for a particular kind of Morse potential and find its normalized eigenfunctions and eigenvalues, exactly. Our work is based on the Laplace transform technique which reduces the second-order differential equation to a first-order.
DOI
10.1088/1674-1137/37/4/043106

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Treatment of NNN-dimensional Schrödinger equation for anharmonic potential via Laplace transform
First time anharmonic potential $V(r)=ar^2+br-\frac{c}{r} \,,(a>0) $ is examined for NNN-dimensional Schrödinger equation via Laplace transformation method. In transformed space, the behavior of the Laplace transform at the singular point of the differential equation is used to study the eigenfunctions and the energy eigenvalues.The results are easy to derive and identical with those obtained by other methods.