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The semiclassical quantization of nonseparable systems using the method of adiabatic switching

1985; American Institute of Physics; Volume: 82; Issue: 10 Linguagem: Inglês

10.1063/1.448719

1520-9032

Rex T. Skodje, F. Borondo, William P. Reinhardt,

Nonlinear Photonic Systems

A method for the semiclassical quantization of multidimensional bound systems based on the adiabatic hypothesis is examined. The validity criteria for multidimensional adiabaticity is discussed. It is demonstrated that the quantizing orbits for nonseparable systems can often be obtained by propagating a single trajectory from well defined initial conditions with a time-dependent Hamiltonian for ∼100 periods. Numerical examples using systems with up to five degrees of freedom are presented and show generally excellent results. It is shown that this method can be used to quantize some states using chaotic trajectories.