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

This article is cited in 16 scientific papers (total in 16 papers)

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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Received: 16.04.1979

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
\by Yu.~M.~Shirokov
\paper Strongly singular potentials in~three-dimensional quantum mechanics
\jour TMF
\yr 1980
\vol 42
\issue 1
\pages 45--49
\jour Theoret. and Math. Phys.
\yr 1980
\vol 42
\issue 1
\pages 28--31

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    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  mathnet  crossref  mathscinet  zmath  isi
    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  mathnet  crossref  mathscinet  zmath  isi
    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  mathnet  crossref  mathscinet  zmath  isi
    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  mathnet  crossref  mathscinet  isi
    5. Yu. G. Shondin, “Three-body problems with $\delta$-functional potentials”, Theoret. and Math. Phys., 51:2 (1982), 434–441  mathnet  crossref  mathscinet  isi
    6. G. K. Tolokonnikov, “Shirokov algebras. I”, Theoret. and Math. Phys., 51:3 (1982), 554–561  mathnet  crossref  mathscinet  zmath  isi  elib
    7. I. S. Tsirova, “Singular potentials in a problem with noncentral interaction”, Theoret. and Math. Phys., 51:3 (1982), 561–563  mathnet  crossref  isi
    8. V. A. Smirnov, “Associative algebra of functionals containing $\delta(x)$ and $r^n$”, Theoret. and Math. Phys., 52:2 (1982), 832–835  mathnet  crossref  mathscinet  zmath  isi
    9. Yu. G. Shondin, “Generalized pointlike interactions in $R_3$ and related models with rational $S$-matrix”, Theoret. and Math. Phys., 64:3 (1985), 937–944  mathnet  crossref  mathscinet  isi
    10. B. S. Pavlov, “The theory of extensions and explicitly-soluble models”, Russian Math. Surveys, 42:6 (1987), 127–168  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. A. K. Motovilov, “Algebraic version of extension theory for a quantum system with internal structure”, Theoret. and Math. Phys., 97:2 (1993), 1217–1228  mathnet  crossref  mathscinet  zmath  isi
    12. Vall, AN, “Fine tuning renormalization and two-particle states in nonrelativistic four-fermion model”, International Journal of Modern Physics A, 12:28 (1997), 5039  crossref  isi
    13. Vall, AN, “Fine-tuning renormalization and two-particle states in the nonrelativistic four-fermion model”, Physics of Atomic Nuclei, 60:8 (1997), 1314  isi
    14. Vall, AN, “Two- and three-particle states in a nonrelativistic four-fermion model in the fine-tuning renormalization scheme: Goldstone mode versus extension theory”, Few-Body Systems, 30:3 (2001), 187  crossref  isi
    15. Shvedov, OY, “Approximations for strongly singular evolution equations”, Journal of Functional Analysis, 210:2 (2004), 259  crossref  isi
    16. E. A. Vedutenko, S. V. Talalov, “About calculation of unperturbative amplitude for the scattering of the quantum particle on a complicated object”, Math. Models Comput. Simul., 2:5 (2010), 597–604  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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