2004•Zeitschrift für Naturforschung AOpen access

Exact Solutions of the N-dimensional Radial Schrödinger Equation with the Coulomb Potential via the Laplace Tranform

Gang Chen

Abstract

The second-order N-dimensional Schrödinger differential equation with the Coulomb potential is reduced to a firstorder differential equation by means of the Laplace transform and the exact bound state solutions are obtained. It is shown that this method solving the Schrödinger equation may serve as a substitute for the factorization approach also in lower dimensions. - PACS numbers: 03.65.Ge.

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Key concepts: Laplace's equation, Laplace transform, Schrödinger equation, Green's function for the three-variable Laplace equation, Bound state, Differential equation, Coulomb, Mathematical analysis