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 TMF, 1980, Volume 42, Number 1, Pages 45–49 (Mi tmf3720)

Strongly singular potentials in three-dimensional quantum mechanics

Yu. M. Shirokov

Abstract: Three-dimensional generalization is obtained for the method proposed in [1] for deriving the one-dimensional Schrödinger equations with strongly singular potentials and positive metric. Exactly solvable examples are presented for renormalizable as well as nonrenormalizable potentials. The generalization is based on the algebra of the threedimensional generalized functions which was constructed in [2].

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English version:
Theoretical and Mathematical Physics, 1980, 42:1, 28–31

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Citation: Yu. M. Shirokov, “Strongly singular potentials in three-dimensional quantum mechanics”, TMF, 42:1 (1980), 45–49; Theoret. and Math. Phys., 42:1 (1980), 28–31

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Yu. M. Shirokov, “Representation of free solutions for Schrödinger equations with strongly singular concentrated potentials”, Theoret. and Math. Phys., 46:3 (1981), 191–196
2. G. K. Tolokonnikov, Yu. M. Shirokov, “Associative algebra of generalized functions closed with respect to differentiation and integration”, Theoret. and Math. Phys., 46:3 (1981), 200–203
3. I. S. Tsirova, Yu. M. Shirokov, “Quantum delta-like potential acting in the $P$ state”, Theoret. and Math. Phys., 46:3 (1981), 203–206
4. S. V. Talalov, Yu. M. Shirokov, “Interaction of a charged particle with an external electromagnetic field in the presence of a strongly singular potential”, Theoret. and Math. Phys., 46:3 (1981), 207–210
5. Yu. G. Shondin, “Three-body problems with $\delta$-functional potentials”, Theoret. and Math. Phys., 51:2 (1982), 434–441
6. G. K. Tolokonnikov, “Shirokov algebras. I”, Theoret. and Math. Phys., 51:3 (1982), 554–561
7. I. S. Tsirova, “Singular potentials in a problem with noncentral interaction”, Theoret. and Math. Phys., 51:3 (1982), 561–563
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13. Vall, AN, “Fine-tuning renormalization and two-particle states in the nonrelativistic four-fermion model”, Physics of Atomic Nuclei, 60:8 (1997), 1314
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