Journal of Experimental and Theoretical Physics

, Volume 95, Issue 4, pp 645–661 | Cite as

Semiclassical approach to states near the potential barrier top

  • V. A. Benderskii
  • E. V. Vetoshkin
  • E. I. Kats
Atoms, Spectra, Radiation


Within the framework of the instanton approach, we present analytical results for the following model problems: (i) particle penetration through a parabolic potential barrier, where the instanton solution practically coincides with the exact (quantum) one; (ii) descriptions of highly excited states in anharmonic potentials of two types: double-well X4 and decay X3. For the former potential, the instanton method accurately reproduces not only single-well and double-well quantization, but also a crossover region (in contrast to the standard WKB approach that fails to describe the crossover behavior); for the latter potential, the instanton method allows studying the resonance broadening and collapse phenomena. We also investigate resonance tunneling that plays a relevant role in many semiconducting devices. We show that the instanton approach gives exact (quantum) results in a broad range of energies. Applications of the method and of the results are applicable to various systems in physics, chemistry, and biology exhibiting double-level behavior and resonance tunneling.


Excited State Potential Barrier Model Problem Relevant Role Crossover Region 
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Copyright information

© MAIK "Nauka/Interperiodica" 2002

Authors and Affiliations

  • V. A. Benderskii
    • 1
    • 2
  • E. V. Vetoshkin
    • 1
  • E. I. Kats
    • 3
    • 4
  1. 1.Institute for Problems of Chemical PhysicsRussian Academy of SciencesMoscow oblast, ChernogolovkaRussia
  2. 2.Lab. Spectrometrie PhysiqueSt. Martin d’Heres, CedexFrance
  3. 3.Institute Laue-LangevinGrenobleFrance
  4. 4.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscow oblast, ChernogolovkaRussia

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