Abstract
In Fock's reciprocal-space treatment of the hydrogen atom,k-space is mapped onto the surface of a 4-dimensional hypersphere, and the solutions (apart from an invariant factor) are 4-dimensional hyperspherical harmonics. Fock's method can be generalized to provide solutions for the Schrödinger equation of a charged particle moving in a many-center Coulomb potential, and in this case the solutions are found by diagonalizing an overlap matrix involving products of hyperspherical harmonics. The present paper discusses a transform which can conveniently be used to evaluate the elements of the overlap matrix.
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Avery, J. Fock transforms in reciprocal-space quantum theory. J Math Chem 15, 233–244 (1994). https://doi.org/10.1007/BF01277562
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DOI: https://doi.org/10.1007/BF01277562