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TMF, 1996, Volume 109, Number 1, Pages 107–123 (Mi tmf1215)  

This article is cited in 9 scientific papers (total in 9 papers)

Solution of spectral problem for Schrödinger equation with degenerate polinomial potential of even power

V. N. Sorokina, A. S. Vshivtsevb, N. V. Norinb

a M. V. Lomonosov Moscow State University
b Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)

Abstract: The symmetry of the stationary Schrödinger equation with a degenerate potential $U(x)=x^{2r}$, $r \in Z_+$, describing phase transitions in quantum systems, is reveled. The analytical procedure of finding the eigenvalues of the potentials in question is constructed and realized numerically for $r=2,3,…,18$. The low energy levels are found.

DOI: https://doi.org/10.4213/tmf1215

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English version:
Theoretical and Mathematical Physics, 1996, 109:1, 1329–1341

Bibliographic databases:

Received: 08.08.1995

Citation: V. N. Sorokin, A. S. Vshivtsev, N. V. Norin, “Solution of spectral problem for Schrödinger equation with degenerate polinomial potential of even power”, TMF, 109:1 (1996), 107–123; Theoret. and Math. Phys., 109:1 (1996), 1329–1341

Citation in format AMSBIB
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\by V.~N.~Sorokin, A.~S.~Vshivtsev, N.~V.~Norin
\paper Solution of spectral problem for Schr\"odinger equation with degenerate polinomial potential of even power
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\vol 109
\issue 1
\pages 107--123
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\zmath{https://zbmath.org/?q=an:0940.34068}
\transl
\jour Theoret. and Math. Phys.
\yr 1996
\vol 109
\issue 1
\pages 1329--1341
\crossref{https://doi.org/10.1007/BF02069892}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. S. Vshivtsev, V. O. Galkin, A. V. Tatarintsev, R. N. Faustov, “Spectral problem for the radial Schrödinger equation with power confining potentials”, Theoret. and Math. Phys., 113:3 (1997), 1530–1542  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. P. Barashev, V. V. Belov, A. S. Vshivtsev, A. G. Kisun'ko, “Some thermodynamic features of ideal systems with nonlinear interaction”, Theoret. and Math. Phys., 116:3 (1998), 1074–1082  mathnet  crossref  crossref  zmath  isi
    3. Vshivtsev, AS, “Algebraic method for solving the spectral problem for nonsymmetric polynomial potentials”, Physics of Atomic Nuclei, 61:9 (1998), 1499  adsnasa  isi
    4. Vshivtsev, AS, “Spectral problem for the radial Schrodinger equation”, Physics of Atomic Nuclei, 61:2 (1998), 169  mathscinet  adsnasa  isi
    5. Vshivtsev, AS, “Solving the spectral problem for the two-dimensional Schrodinger equation with nonseparable variables”, Physics of Atomic Nuclei, 62:2 (1999), 245  mathscinet  adsnasa  isi
    6. O. S. Pavlova, A. R. Frenkin, “Radial Schrödinger equation: The spectral problem”, Theoret. and Math. Phys., 125:2 (2000), 1506–1515  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. V. A. Vshivtsev, A. V. Prokopov, A. V. Tatarintsev, “Some features of the thermodynamics of nonlinear classical systems”, Theoret. and Math. Phys., 125:2 (2000), 1568–1577  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. Faustov, RN, “Algebraic approach to the spectral problem for the Schrodinger equation with power potentials”, International Journal of Modern Physics A, 15:2 (2000), 209  crossref  zmath  adsnasa  isi  scopus  scopus  scopus
    9. Kvitko G.V., Kuzin E.L., Shot D.V., “Chislennoe reshenie uravneniya shredingera s polinomialnymi potentsialami (chast i)”, Vestnik Baltiiskogo federalnogo universiteta im. I. Kanta, 2011, no. 5, 115–119  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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