The semiclassical propagator for the one-dimensional anharmonic oscillator is investigated, in the configuration space, by means of the so-called Van Vleck formula, which expresses it as a sum over all the denumerably infinite classical paths connecting given points in the same time. Analytical formulae for the paths' contributions are given, together with some numerical results. It is shown that in the general case the amplitudes of the contributions asymptotically approach the same value, while the phases oscillate; the Van Vleck series therefore does not converge, but in the generic case it can be resummed. Finally, the conditions under which one of the paths gives a dominant contribution to the semiclassical propagator are discussed.

ON THE SEMICLASSICAL PROPAGATOR FOR THE ANHARMONIC-OSCILLATOR

FUSCO GIRARD, Mario
1992

Abstract

The semiclassical propagator for the one-dimensional anharmonic oscillator is investigated, in the configuration space, by means of the so-called Van Vleck formula, which expresses it as a sum over all the denumerably infinite classical paths connecting given points in the same time. Analytical formulae for the paths' contributions are given, together with some numerical results. It is shown that in the general case the amplitudes of the contributions asymptotically approach the same value, while the phases oscillate; the Van Vleck series therefore does not converge, but in the generic case it can be resummed. Finally, the conditions under which one of the paths gives a dominant contribution to the semiclassical propagator are discussed.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/3366079
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