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arXiv:2308.11653

A theorem for the normalization of continuous spectrum stationary states

German Kälbermann

Published Aug 20, 2023• 0 citations
arXivHTMLPDF

Abstract

We present analytic formulae that simplify the evaluation of the normalization of continuous spectrum stationary states in the one-dimensional Schrödinger equation.
DOI
10.48550/arxiv.2308.11653

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We propose a new simplified procedure for finding the analytical solutions of the stationary one-dimensional Schrödinger equation, with asymmetric boundary conditions imposed on the equation.The essence of the method consists in expressing the general solution explicitly in terms of the boundary parameters in a form which, by itself, satisfies one of the boundary conditions involved; then, the other boundary condition gives straightforwardly the characteristic equation.This method may turn out to be beneficial with regard to the recently growing interest in one-dimensional quantum systems.