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Singular Potentials
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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Citations
Cited by
Below the Breitenlohner-Freedman bound in the nonrelativistic AdS/CFT correspondence
Moroz, S. (2010) · Physical Review D · doi:10.1103/physrevd.81.066002 · Cited by 31
Metadata
- Authors
- Case, K. M.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1950-12-01
- Volume
- 80
- Issue
- 5
- Pages
- 797-806
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W4234941667
- Cited by
- 504
- References
- 0
- FWCI
- 3.00
- Type
- journal article
- Language
- en
- Open access
- closed
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- Case, K. M. (1950). Singular Potentials. Physical Review. https://doi.org/10.1103/physrev.80.797
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
