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TMF, 1988, Volume 74, Number 3, Pages 331–344 (Mi tmf4422)  

This article is cited in 14 scientific papers (total in 14 papers)

Quantum-mechanical models in $R_n$ associated with extensions of the energy operator in a Pontryagin space

Yu. G. Shondin

Abstract: The paper describes self-adjoint extensions of the operator $H_0=-\Delta$ from the Hilbert space $L_2(R_n)$ to a certain Pontryagin space generated by “interactions” represented by generalized functions. Hamiltonians of quantum-mechanical models are obtained by restricting such extensions to positive invariant subspaces.

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English version:
Theoretical and Mathematical Physics, 1988, 74:3, 220–230

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Received: 25.11.1985
Revised: 01.10.1986

Citation: Yu. G. Shondin, “Quantum-mechanical models in $R_n$ associated with extensions of the energy operator in a Pontryagin space”, TMF, 74:3 (1988), 331–344; Theoret. and Math. Phys., 74:3 (1988), 220–230

Citation in format AMSBIB
\by Yu.~G.~Shondin
\paper Quantum-mechanical models in~$R_n$ associated with extensions of the energy operator in a~Pontryagin space
\jour TMF
\yr 1988
\vol 74
\issue 3
\pages 331--344
\jour Theoret. and Math. Phys.
\yr 1988
\vol 74
\issue 3
\pages 220--230

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    This publication is cited in the following articles:
    1. A. A. Kiselev, I. Yu. Popov, “Higher moments in a model of zero-width slits”, Theoret. and Math. Phys., 89:1 (1991), 1019–1024  mathnet  crossref  mathscinet  isi
    2. I. Yu. Popov, “The Helmholtz resonator and the theory of operator extensions in a space with indefinite metric”, Russian Acad. Sci. Sb. Math., 75:2 (1993), 285–315  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Theoret. and Math. Phys., 92:3 (1992), 1032–1037  mathnet  crossref  mathscinet  zmath  isi
    4. 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
    5. I. Yu. Popov, “Stratified flow in electric field, Schrödinger equation and operator extension theory model”, Theoret. and Math. Phys., 103:2 (1995), 535–542  mathnet  crossref  mathscinet  zmath  isi
    6. K. A. Makarov, V. V. Melezhik, A. K. Motovilov, “The point interactions in the problem of three quantum particles with internal structure”, Theoret. and Math. Phys., 102:2 (1995), 188–207  mathnet  crossref  mathscinet  zmath  isi
    7. A. A. Kiselev, I. Yu. Popov, “Indefinite metric and scattering by a domain with a small hole”, Math. Notes, 58:6 (1995), 1276–1285  mathnet  crossref  mathscinet  zmath  isi
    8. I. Yu. Popov, D. A. Zubok, “Two physical applications of the Laplace operator perturbed on a null set”, Theoret. and Math. Phys., 119:2 (1999), 629–639  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. Yu. G. Shondin, “Singular point perturbations of an odd operator in a $\mathbb Z_2$-graded space”, Math. Notes, 66:6 (1999), 764–776  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. O. Yu. Shvedov, “Exactly solvable quantum mechanical models with Stückelberg divergences”, Theoret. and Math. Phys., 125:1 (2000), 1377–1390  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. 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
    12. Shvedov, OY, “Exactly solvable quantum mechanical models with infinite renormalization of the wavefunction”, Journal of Physics A-Mathematical and General, 34:16 (2001), 3483  crossref  isi
    13. Kurasov, P, “On field theory methods in singular perturbation theory”, Letters in Mathematical Physics, 64:2 (2003), 171  crossref  isi
    14. Shvedov, OY, “Approximations for strongly singular evolution equations”, Journal of Functional Analysis, 210:2 (2004), 259  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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