A path-integral approach to expectation values in time-dependent problems

Abstract

Within the framework of Feynman path integration, expectation values of quantum mechanical operators may be exactly obtained for a class of time-dependent problems. Attention is focused on the two-dimensional motion of a charged particle in a perpendicular magnetic field with a time-dependent driving force. A harmonic oscillator potential is included to ensure that the corresponding density matrix is properly defined although some expectation values are defined without it. This potential is at least a mathematical convenience. Some discussion concerning the conditions under which steady states may be attained is also included.