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Prog. Theor. Phys. Vol. 86 No. 2 (1991) pp. 443-467

[ Full Text PDF : FREE ACCESS (1153K) ]

Time-Dependent Variational Approach in Terms of Squeezed Coherent States

Yasuhiko Tsue and Yoshikazu Fujiwara

Department of Physics, Kyoto University, Kyoto 606

(Received March 14, 1991)

Abstract:

A general framework for a time-dependent variational approach in terms of squeezed coherent states is given with the aid of canonicity conditions developed in the time-dependent Hartree-Fock theory. By using a formula given by Balian and Brezin for canonical decompositions of generalized Bogoliubov transformations, we show that this approach is entirely equivalent to that given by Jackiw and Kerman in terms of the most general Gaussian functions, which is originally motivated for the variational definition of the effective action in the quantum field theory. The resultant equations of motion have structure of classical Hamiltonian systems consisting of displacement degree of freedom and squeezing degree of freedom in the configuration space. The initial conditions for solving these equations, particularly for the squeezing degree of freedom, are discussed in connection with the minimum-uncertainty relations of the squeezed coherent state. For a simple one-dimensional quantum-mechanical Hamiltonian with potentials of quadratic terms or less, the present formulation gives an exact result for the time-evolution of the Gaussian wave packet.


URL : http://ptp.ipap.jp/link?PTP/86/443/
DOI : 10.1143/PTP.86.443

[ Full Text PDF : FREE ACCESS (1153K) ] Citation:

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