Dynamical symmetry of nonstationary systems

Abstract

The problem of the symmetry of equations and that of the dynamical 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 anyN-dimensional quantum system with a quadratic Hamiltonian is obtained as theUN,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 representations of groups. In the general case of a quadratic Hamiltonian this group is the group of motion of theN-dimensional non-Euclidean complex space. In greater detail, a charged-particle motion in a uniform time-dependent electromagnetic field, anN-dimensional generalized oscillator and a three-dimensional charged oscillator in electromagnetic field are considered.