Singular Potentials

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Abstract
The difficulties arising in quantum mechanics when the potential is highly singular are considered. It is found that the Hamiltonian needs further specification in such cases. This may be done conveniently by requiring a fixed phase for the wave functions at the origin. A proof that all the well-known singular examples are amenable to this treatment is given. For illustration the spectra for spin zero and one-half particles in the fields of highly charged nuclei are found. It is also shown that a complete set of eigenfunctions for a vector particle in a Coulomb field can be found.

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