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Teimuraz P. Nadareishvili

Publications and source records attributed to Teimuraz P. Nadareishvili.

6 recordsLinked to original sources
arXiv2011

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

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.

quant-ph↗
arXiv2010

Status of the Radial Schrodinger Equation

We show that equation for radial wave function in its traditional form is compatible with the full Schrodinger equation if and only if a definite additional constraint required. This constraint has a boundary condition form at the origin. Some of consequences are also discussed.

math-ph↗
arXiv2010

Unexpected Delta-Function Term in the Radial Schrodinger Equation

Careful exploration of the idea that equation for radial wave function must be compatible with the full Schrodinger equation shows appearance of the delta-function while reduction of full Schrodinger equation in spherical coordinates. Elimination of this extra term produces a boundary condition for the radial wave function, which is the same both for regular and singular potentials.

math-ph↗