Prog. Theor. Phys. Vol. 77 No. 3 (1987) pp. 517-547
Semi-Classical Quantization for Multi-Dimensional Coupled-Channel Equation
Department of Physics, Kyoto University, Kyoto 606
(Received May 9, 1986)
Multi-dimensional coupled-channel equation is treated by the WKB approximation for the main purpose of deriving the semi-classical quantization rule for it. A somewhat general type of the multi-dimensional coupled-channel Hamiltonian is presented which enables us to derive the semiclassical quantization rule for the energy spectra. As in the one-dimensional case, the WKB wave function has an additional phase besides the usual phase \intΣps dxs, and the quantization rule should include the contribution from this additional phase. The structure of the WKB wave function in the adiabatic representation is also discussed.
DOI : 10.1143/PTP.77.517
- K. Yabana and H. Horiuchi, Prog. Theor. Phys. 71 (1984), 1275[PTP].
H. L. Berk and D. Pfirsch, J. Math. Phys. 21 (1980), 2054[CrossRef].
- K. Yabana and H. Horiuchi, Prog. Theor. Phys. 75 (1986), 592[PTP].
- M. V. Berry, Proc. R. Soc. London A392 (1984), 45.
B. Simon, Phys. Rev. Lett. 51 (1983), 2167[APS].
H. Kuratsuji and S. Iida, Prog. Theor. Phys. 74 (1985), 439[PTP].
- V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, New York, 1978).
- J. H. Van Vleck, Proc. Natl. Acad. Sci. 14 (1928), 178.