The hydrogen atom in spheroidal coordinates: the continuous spectrum

Author: Tsotne Gamsakhurdashvili
Keywords: Coulomb field, spheroidal coordinates, continuous spectrum
Annotation:

The problem of the hydrogen atom in prolate spheroidal coordinates is solved for the continuous spectrum. For the first time, Coulomb spheroidal functions are obtained on exact solution of the appropriate one-dimensional equations, which are shown to be Heun’s confluent equations. The derived functions are a natural generalization of the well-known Coulomb wave functions of the continuous spectrum obtained in spherical polar coordinates. An application of the elaborated approach for the algebraic solution of the two-Coulomb center problem for the continuous spectrum is discussed.

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