11 research outputs found
Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields
We construct an explicit solution of the Cauchy initial value problem for the
time-dependent Schroedinger equation for a charged particle with a spin moving
in a uniform magnetic field and a perpendicular electric field varying with
time. The corresponding Green function (propagator) is given in terms of
elementary functions and certain integrals of the fields with a characteristic
function, which should be found as an analytic or numerical solution of the
equation of motion for the classical oscillator with a time-dependent
frequency. We discuss a particular solution of a related nonlinear Schroedinger
equation and some special and limiting cases are outlined.Comment: 17 pages, no figure
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