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Open Quantum Systems Decoherence

What is the boundary condition for radial wave function of the Schrödinger equation ?

arXiv

Authors: Anzor A. Khelashvili, Teimuraz P. Nadareishvili

Year

2010

Paper ID

11274

Status

Preprint

Abstract Read

~2 min

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Abstract

There is much discussion in the mathematical physics literature as well as in quantum mechanics textbooks on spherically symmetric potentials. Nevertheless, there is no consensus about the behavior of the radial function at the origin, particularly for singular potentials. A careful derivation of the radial Schrödinger equation leads to the appearance of a delta function term when the Laplace operator is written in spherical coordinates. As a result, regardless of the behavior of the potential, an additional constraint is imposed on the radial wave function in the form of a vanishing boundary condition at the origin.

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This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
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There is much discussion in the mathematical physics literature as well as in quantum mechanics textbooks on spherically symmetric potentials.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1009.2694 [2] arXiv https://arxiv.org/abs/1009.2694 [3] Publisher https://arxiv.org/abs/1009.2694

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