Prog. Theor. Phys. Vol. 75 No. 3 (1986) pp. 592-618
Adiabatic Viewpoint for the WKB Treatment of Coupled Channel System
— Appearance of the Berry Phase and Another Extra Phase Accompanying the Adiabatic Motion
Department of Physics, Kyoto University, Kyoto 606
(Received June 27, 1985)
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, Hij(x,x')≠Hij(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.
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