Integrals of motion of nonstationary quantum systems

V. V. Dodonov, Vladimir I. Man’ko

Vladimir I. Man’ko

Fyodor Malikov

Octavio Castaños, Ramón López–Peña, Vladimir I. Man’ko

The time-dependent integrals of motion, linear in position and momentum operators, of a quantum system are extracted from Noether's theorem prescription by means of special time-dependent variations of coordinates. For the stationary case of the generalized two-dimensional harmonic oscillator, the time-independent integrals of motion are shown to correspond to special Bragg-type symmetry properties. A detailed study for the nonstationary case of this quantum system is presented. The linear integrals of motion are constructed explicitly for the case of varying mass and coupling strength. They are also obtained from Noether's theorem. The general treatment for a multi-dimensional quadratic system is indicated and it is shown that the time-dependent variations that give rise to the linear invariants, as conserved quantities, satisfy the corresponding classical homogeneous equations of motion for the coordinates.

M. A. Markov

Aghayeva Rana Gazanfar

A modified factorization method for a charged particle in a time-dependent magnetic field has been developed by virtue of motion quantum integrals. Application of this method to the considered system helps to find exact solutions for a range of nonstationary potentials.