Prog. Theor. Phys. Vol. 75 No. 3 (1986) pp. 592-618

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Adiabatic Viewpoint for the WKB Treatment of Coupled Channel System

— Appearance of the Berry Phase and Another Extra Phase Accompanying the Adiabatic Motion —

Kazuhiro Yabana and Hisashi Horiuchi

Department of Physics, Kyoto University, Kyoto 606

(Received June 27, 1985)

Abstract:

WKB approximation for the coupled channel equation with non-local interaction, presented previously, is discussed by putting emphasis on the relation to the adiabatic approximation. When the off-diagonal elements of the Hamiltonian is not symmetric, H_ij(x,x')≠H_ij(x',x), an additional phase besides the usual phase (i/\hbar)\intp(x)dx appears in the WKB wave function, which is the first order in Planck's constant. For the bound state, this additional phase modifies the Bohr-Sommerfeld quantization condition. Expressing it by adiabatic quantities, it is shown that it includes the so-called Berry phase as a part but is not exhausted by the Berry phase. An analysis of a simple schematic model shows that the inclusion of this additional phase to hte quantization condition is important to reproduce the quantum energy spectrum.

URL : http://ptp.ipap.jp/link?PTP/75/592/
DOI : 10.1143/PTP.75.592

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Citing Article(s) :

Progress of Theoretical Physics Vol. 77 No. 3 (1987) pp. 517-547 :
Semi-Classical Quantization for Multi-Dimensional Coupled-Channel Equation

Kazuhiro Yabana and Hisashi Horiuchi
Progress of Theoretical Physics Vol. 87 No. 3 (1992) pp. 627-649 :
Analysis of Dynamical Effects on Geometric Phase by Means of Time-Dependent Variational Principle

Takahiro Fukui and Yasuhiko Tsue
Progress of Theoretical Physics Vol. 87 No. 4 (1992) pp. 927-935 :
On the Extra Phase Accompanying Berry's Phase in Terms of Coherent State Path Integral

Takahiro Fukui