Generalised spheroidal wave equations for a hydrogenic system in half space. I. General properties

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Abstract
The qualitative properties of the generalised spheroidal wave equations for a hydrogenic system in half space obtained previously are studied. Geometrical and dynamical symmetry properties are discussed briefly. The behaviour of the energy eigenvalue and the eigenvalue of a constant of the motion, Omega , in the limiting cases d=0 and d= infinity are investigated, where d is the distance between the centre of the system and the boundary surface. The property that the number of nodes of the wavefunction in each coordinate is conserved is used to find the correlations between the quantum numbers as well as the energy eigenvalue at d=0 and those at d= infinity .

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