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TMF, 1982, Volume 50, Number 3, Pages 390–396 (Mi tmf2307)  

This article is cited in 15 scientific papers (total in 15 papers)

Quasiclassical trajectory-coherent states of a nonrelativistic particle in an arbitrary electromagnetic field

V. G. Bagrov, V. V. Belov, I. M. Ternov


Abstract: It is shown that for a nonrelativistic charged particle moving in an arbitrary external electromagnetic field there exist approximate solutions of the Schrödinger equation such that the mean quantum-mechanical coordinates and momenta of these states are enact general solutions of the classical Hamilton equations. Such states are called trajectory-coherent states. The wave functions of trajectory-coherent states are obtained by Maslov's complex germ method. The simplest properties of these states are studied.

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English version:
Theoretical and Mathematical Physics, 1982, 50:3, 256–261

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Received: 20.04.1981

Citation: V. G. Bagrov, V. V. Belov, I. M. Ternov, “Quasiclassical trajectory-coherent states of a nonrelativistic particle in an arbitrary electromagnetic field”, TMF, 50:3 (1982), 390–396; Theoret. and Math. Phys., 50:3 (1982), 256–261

Citation in format AMSBIB
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\paper Quasiclassical trajectory-coherent states of a~nonrelativistic particle in an~arbitrary electromagnetic field
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\vol 50
\issue 3
\pages 390--396
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\jour Theoret. and Math. Phys.
\yr 1982
\vol 50
\issue 3
\pages 256--261
\crossref{https://doi.org/10.1007/BF01016454}
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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. V. P. Maslov, “Non-standard characteristics in asymptotic problems”, Russian Math. Surveys, 38:6 (1983), 1–42  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. A. Bobrov, O. F. Dorofeev, G. A. Chizhov, “Synchrotron radiation of an electron in a coherent state”, Theoret. and Math. Phys., 61:2 (1984), 1149–1154  mathnet  crossref  isi
    3. V. G. Bagrov, V. V. Belov, “Semiclassical method of calculating the characteristics of the spontaneous radiation of a charge moving in periodic structures”, Theoret. and Math. Phys., 70:3 (1987), 330–336  mathnet  crossref  isi
    4. V. G. Bagrov, V. V. Belov, “Time of loss of a specified accuracy of semiclassical trajectory-coherent states”, Theoret. and Math. Phys., 74:2 (1988), 211–213  mathnet  crossref  mathscinet  isi
    5. V. V. Belov, S. Yu. Dobrokhotov, “Semiclassical maslov asymptotics with complex phases. I. General approach”, Theoret. and Math. Phys., 92:2 (1992), 843–868  mathnet  crossref  mathscinet  isi
    6. V. G. Bagrov, V. V. Belov, A. M. Rogova, “Semiclassically concentrated quantum states”, Theoret. and Math. Phys., 90:1 (1992), 55–61  mathnet  crossref  mathscinet  isi
    7. V. V. Belov, M. F. Kondrat'eva, ““Classical” equations of motion in quantum mechanics with gauge fields”, Theoret. and Math. Phys., 92:1 (1992), 722–735  mathnet  crossref  mathscinet  isi
    8. V. G. Bagrov, V. V. Belov, M. F. Kondrat'eva, “The semiclassical approximation in quantum mechanics. A new approach”, Theoret. and Math. Phys., 98:1 (1994), 34–38  mathnet  crossref  mathscinet  zmath  isi
    9. V. V. Belov, A. Yu. Trifonov, A. V. Shapovalov, “Semiclassical Trajectory-Coherent Approximations of Hartree-Type Equations”, Theoret. and Math. Phys., 130:3 (2002), 391–418  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. O. Yu. Shvedov, “Maslov Complex Germ Method for Systems with First-Class Constraints”, Theoret. and Math. Phys., 136:3 (2003), 1258–1272  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. O. Yu. Shvedov, “Relativistically Covariant Quantum Field Theory of the Maslov Complex Germ”, Theoret. and Math. Phys., 144:3 (2005), 1296–1314  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. Alexey Borisov, Alexander Shapovalov, Andrey Trifonov, “Transverse Evolution Operator for the Gross–Pitaevskii Equation in Semiclassical Approximation”, SIGMA, 1 (2005), 019, 17 pp.  mathnet  crossref  mathscinet  zmath
    13. Belov, VV, “Semiclassical spectrum for a Hartree-type equation corresponding to a rest point of the Hamilton-Ehrenfest system”, Journal of Physics A-Mathematical and General, 39:34 (2006), 10821  crossref  isi
    14. V. V. Belov, F. N. Litvinets, A. Yu. Trifonov, “Semiclassical spectral series of a Hartree-type operator corresponding to a rest point of the classical Hamilton–Ehrenfest system”, Theoret. and Math. Phys., 150:1 (2007), 21–33  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    15. A. Yu. Anikin, S. Yu. Dobrokhotov, A. I. Klevin, B. Tirozzi, “Gausian packets and beams with focal points in vector problems of plasma physics”, Theoret. and Math. Phys., 196:1 (2018), 1059–1081  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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