9 research outputs found
Quantum Integrals of Motion for Variable Quadratic Hamiltonians
We construct the integrals of motion for several models of the quantum damped
oscillators in nonrelativistic quantum mechanics in a framework of a general
approach to the time-dependent Schroedinger equation with variable quadratic
Hamiltonians. An extension of Lewis-Riesenfeld dynamical invariant is given.
The time-evolution of the expectation values of the energy related positive
operators is determined for the oscillators under consideration. A proof of
uniqueness of the corresponding Cauchy initial value problem is discussed as an
application.Comment: 32 pages, no figure