SEMICLASSICAL APPROACH TO STATES NEAR THE POTENTIAL BARRIER TOP
Benderskii V.A., Vetoshkin E.V., Kats E.I.

Поступила в редакцию: 30 Мая 2002

PACS: 05.45.-a, 05.45.Gg

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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.