Abstract
The Schrodinger equation for a hydrogen atom can be solved in spherical polar, parabolic and spheroidal coordinates. Relations between these types of solution are obtained by an algebraic method depending on the existence of an extra constant of the motion for the two-centre Kepler problem. Limiting conditions and certain orthogonality relations are studied. It is shown that, in Fock's method of stereographic projection of momentum space onto the surface of a four-dimensional hypersphere, one cannot find an orthogonal coordinate system to separate the equations of motion, corresponding to the use of spheroidal coordmates in configuration space. This is in marked contrast with the situation with spherical polar and parabolic coordinates.
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