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TMF, 1999, Volume 120, Number 1, Pages 99–115 (Mi tmf763)  

This article is cited in 6 scientific papers (total in 6 papers)

The reduced semiclassical description method

A. A. Lobashev, N. N. Trunov

D. I. Mendeleev Institute for Metrology

Abstract: We develop a new version of the semiclassical analysis of a system of bound states in centrally symmetrical potentials. The set of potentials is in a $1:1$ correspondence with a certain set of pairs of functions of the orbital momentum. The first of these functions determines the usual WKB quantization condition and groups the potentials into equivalence classes. Its Mellin transform demonstrates similar behavior for the typical potentials, which allows describing the equivalence class with a small number of parameters. We can chose these parameters as the asymptotically exact estimates of the number of states. We obtain an equation that allows classifying states in a self-consistent atomic potential without knowing the explicit form of the potential. The second of these functions distinguishes the potentials within an equivalence class and also gives the first correction to the quantization condition.

DOI: https://doi.org/10.4213/tmf763

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English version:
Theoretical and Mathematical Physics, 1999, 120:1, 896–909

Bibliographic databases:

Received: 13.01.1999

Citation: A. A. Lobashev, N. N. Trunov, “The reduced semiclassical description method”, TMF, 120:1 (1999), 99–115; Theoret. and Math. Phys., 120:1 (1999), 896–909

Citation in format AMSBIB
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\paper The reduced semiclassical description method
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\jour Theoret. and Math. Phys.
\yr 1999
\vol 120
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\pages 896--909
\crossref{https://doi.org/10.1007/BF02557399}
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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. A. Lobashev, N. N. Trunov, “An integral semiclassical method for calculating the spectra for centrally symmetric potentials”, Theoret. and Math. Phys., 124:3 (2000), 1250–1264  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Tarbeev, YV, “The periodic system and the metrology of mesoscopic quantum systems”, Measurement Techniques, 44:9 (2001), 944  crossref  isi  scopus  scopus  scopus
    3. Tarbeyev Y.V., Trunov N.N., Lobashev A.A., Kukhar V.V., “Effective quantum number for centrally symmetric potentials”, Operator Methods in Ordinary and Partial Differential Equations, Operator Theory : Advances and Applications, 132, 2002, 403–410  mathscinet  zmath  isi
    4. K. S. Mamaeva, N. N. Trunov, “Wave Equations in Riemannian Spaces”, Theoret. and Math. Phys., 135:1 (2003), 520–530  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. N. N. Trunov, “A Class of Potentials for Which Exact Semiclassical Quantization Can Be Achieved”, Theoret. and Math. Phys., 138:3 (2004), 407–417  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. Lobashev, AA, “A universal effective quantum number for centrally symmetric problems”, Journal of Physics A-Mathematical and Theoretical, 42:34 (2009), 345202  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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