Energy splitting in a finite periodic multiple-well potential
نویسندگان
چکیده
منابع مشابه
Energy splitting in symmetric double-well potentials
The quantum mechanical tunnelling in a smooth symmetric double-well potential is a long-standing and well-known problem. Three methods have been proposed to calculate the energy splitting: the instanton method @1,2#, the WKB approximation @3,4# and numerical calculation @4–6#. The instanton method is helpful to understand the physical insight of quantum tunnelling, but the validity is restricte...
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We investigate the effect of anharmonicity on the WKB approximation in a double well potential. By incorporating the anharmonic perturbation into the WKB energy splitting formula we show that the WKB approximation can be greatly improved in the region over which the tunneling is appreciable. We also observe that the usual WKB results can be obtained from our formalism as a limiting case in whic...
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The accuracy of the WKB approximation when predicting the energy splitting of bound states in a double well potential is the main subject of this paper. The splitting of almost degenerate energy levels below the top of the barrier results from the tunneling and is thus supposed to be exponentially small. By using the standard WKB quantization we deduce an analytical formula for the energy split...
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Semiclassical quantization is very useful to understand the global behaviour of eigenfunctions and energy spectra of quantum systems, since it allows us to obtain analytic expressions. The leading semiclassical approximation (torus quantization) is just the first term of a certain h̄–expansion, which is called WKB (Maslov and Fedoriuk 1981). A systematic study of the accuracy of semiclassical ap...
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ژورنال
عنوان ژورنال: European Journal of Physics
سال: 2017
ISSN: 0143-0807,1361-6404
DOI: 10.1088/1361-6404/aa7b68