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Coherent States and Transition Probabilities in a Time-Dependent
Electromagnetic Field
I. A. Malkin, V. I. Man'ko, and D. A. Trifonov
P. N. Lebedev Institute of Physics, Moscow,
U. S. S. R.
Received 26 May 1970
Abstract. - New time-dependent invariants for the N-dimensional
nonstationary
harmonic oscillator and for a charged particle in a varying axially
symmetric
classical electromagnetic field are found. For these quantum systems,
coherent states are introduced, and the Green's functions are obtained
in
closed form. For a special type of electromagnetic field which is constant
in the remote past and future, the transition amplitudes between both
arbitrary coherent states and energy eigenstates are calculated and
expressed in terms of classical polynomials. The adiabatic approximation
and adiabatic invariants are discussed. In the special case of a particle
with time-dependent mass, the solution of the Schroedinger equation
is
found. The symmetry of nonstationary Hamiltonians is discussed, and
the
noncompact group U(N, 1) is shown to be the group of dynamical symmetry
for
the time-dependent N-dimensional oscillator.
©1970 The American Physical Society
URL: http://publish.aps.org/abstract/PRD/v2/p1371 ( PDF 2181 kB)
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