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

Kevin Zelaya

doi:10.14311/AP.2022.62.0211

Authors

Kevin Zelaya Czech Academy of Science, Nuclear Physics Institute, 250 68 Řež, Czech Republic

DOI:

https://doi.org/10.14311/AP.2022.62.0211

Keywords:

Time-dependent mass oscillators, Caldirola-Kanai oscillator, quantum invariants, coherent states, semiclassical dynamics

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 conventional
Caldirola-Kanai case.

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