Prog. Theor. Phys. Vol. 79 No. 2 (1988) pp. 480-492

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Semiclassical Description of Bound State Wave Functions for Integrable Systems

— R(4) Model —

Research Center for Nuclear Physics, Osaka University, Ibaraki 567
^*Research Division, Hamamatsu Photonics, Hamamatsu 435

(Received September 21, 1987)

Abstract:

Semiclassical wave functions of bound states are constructed for an integrable model having R(4) ≃SU(2) ⊗SU(2) symmetry. Each eigenstate is expressed as an integral of generalized coherent states over a quantized torus, which satisfies a standard Einstein-Brillouin-Keller quantization condition. Obtained wave functions as well as transition rates are compared with those of exact solutions calculated via diagonalization. Semiclassical and exact results show a close correspondence over a broad range of the parameters in the model.

URL : http://ptp.ipap.jp/link?PTP/79/480/
DOI : 10.1143/PTP.79.480

References:

J. W. Negele, Rev. Mod. Phys. 54 (1982), 913[APS].
T. Suzuki and H. Kuratsuji, in Lecture Notes in Physics 171, ed. K. Goeke et al. (Springer, Berlin, 1982), p. 254.
H. Kuratsuji, Phys. Lett. 108B (1982), 367.
Other studies of quantized wave functions may be found e.g., in,
N. DeLeon and E. J. Heller, J. Chem. Phys. 78 (1983), 4005[CrossRef].
R. G. Littlejohn, Phys. Rev. Lett. 56 (1986), 2000[APS].
H. Kuratsuji and T. Suzuki, Phys. Lett. 92B (1980), 19.
See also, A. Perelomov, Generalized Coherent States and Their Applications (Springer, Berlin, 1986).
T. Suzuki, Nucl. Phys. A398 (1983), 557.
For instance, K. Matsuyanagi, Prog. Theor. Phys. 67 (1982), 1441[PTP].
Y. Mizobuchi, Prog. Theor. Phys. 65 (1981), 1450[PTP].
J. Radcliffe, J. of Phys. A4 (1971), 313[IoP STACKS].
F. T. Arrecchi, E. Courtens, R. Gilmore and H. Thomas, Phys. Rev. A6 (1972), 2211[APS].

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