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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2005

Quantum and semiclassical phase functions for the quantization of symmetric oscillators

Résumé

We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schrödinger equation. For anharmonic oscillators, first-order semiclassical quantization is seldom accurate and the higher order expansions eventually break down given the asymptotic nature of the series. A quantum phase that allows us in principle to retrieve the exact quantum mechanical quantization condition and wavefunctions is given along with an iterative scheme to compute it. The arbitrariness surrounding quantum phase functions is lifted by supplementing the phase with boundary conditions involving high order semiclassical expansions. This allows us to extend the definition of oscillation numbers, which determine the quantization of the harmonic oscillator, to the anharmonic case. Several illustrations involving homogeneous as well as coupling constant dependant anharmonic oscillators are given.

Dates et versions

hal-00961304 , version 1 (19-03-2014)

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Citer

A. Matzkin, M. Lombardi. Quantum and semiclassical phase functions for the quantization of symmetric oscillators. Journal of Physics A: Mathematical and Theoretical, 2005, 38, pp.6211-6230. ⟨10.1088/0305-4470/38/27/008⟩. ⟨hal-00961304⟩
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