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

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

2010-09-14

arxiv.org/abs/1009.2694v2

Am.J.Phys. 79:668-671,2011

Physics

Quantum Physics

15 pages

Scientific paper

10.1119/1.3546099

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 Schr\"odinger 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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