Time-dependent mass oscillators: constants of motion and semiclasical states

Abstract

This work reports the construction of constants of motion for a family of time-dependent mass oscillators, achieved by implementing the formalism of form-preserving point transformations. The latter allows obtaining a spectral problem for each constant of motion, one of which leads to a non-orthogonal set of eigensolutions that are, in turn, coherent states. That is, eigensolutions whose wavepacket follows a classical trajectory and saturate, in this case, the Schrödinger-Robertson uncertainty relationship. Results obtained in this form are relatively general, and some particular examples are considered to illustrate the results further. Notably, a regularized Caldirola-Kanai mass term is introduced in an attempt to amend some of the unusual features found in the conventionalCaldirola-Kanai case.