IL NUOVO CIMENTO   Vol. 4 A, N. 4    21 Agosto 1971

     Dynamical Symmetry of Nonstationary Systems

          I.A. Malkin, V.I. Man'ko and D.A. Trifonov
         P.N. Lebedev Institute of Physics - Moscow

         (ricevuto l'8 Febbraio 1971)

Summary. -- The problem of the symmetry of equations and that of the
dymical symmetry of nonstationary quantum systems are discussed and some
particular cases are considered. It is shown that the dynamical symmetry
group is the same both for stationary and nonstationary systems. The
dynamical symmetry group for any N-dimensional quantum system with a
quadratic Hamiltonian is obtained as the U(N,1) group. For the systems
which are stationary in the remote past and future the transition
amplitudes between initial and final states may be regarded as matrix
elements of representation of groups. In the general case of a quadratic
Hamiltonian this group is the group of motion of the N-dimensional
non-Euclidean complex space. In greater detail, a charged-particle motion
in a uniform time-dependent electromagnetic field, an N-dimensional
generalized oscillator and a three-dimensional charged oscillator in
electromagnetic field are considered.