On the rotating-harmonic-oscillator equation

George P. Flessas

Mohsen Daeimohammad

The aim of the present study is to investigate the effect of the counter-rotating terms on the quantum dynamics of a harmonic oscillator in the presence of a deformed bath. We first obtain the Langevin equation of motion for damped oscillator with and without the rotating-wave approximation (RWA). Then, we study the effect of the counter-rotating terms on the diffusion coefficients. Then, we obtain the equation of motion for the harmonic oscillator correlation function with and without the RWA. Finally, we investigate the influence of the counter-rotating terms on the oscillator correlation function.

Ettore Salusti B, Francesco Zirilli

P. R. Berman

Three calculations of optical Faraday rotation are presented in which a linearly polarized field is incident on a medium of harmonic oscillators in the presence of a longitudinal magnetic field. The rotation of the plane of polarization of the field is evaluated using classical oscillators and the Lorentz force equation, quantum oscillators and the Heisenberg equations of motion, and quantum oscillators and a Schrödinger equation approach. It is shown that a simple argument, based on the assumption that a circularly polarized field drives either Δm=1 or Δm=−1 transitions on absorption (m is the magnetic quantum number), leads to an incorrect result for the Verdet constant.

M. Lakshmanan

Mohammed A. Z. Habeeb

Exact coherent states for a particle moving in a cranked anisotropic harmonic oscillator potential are constructed and their properties investigated. It is found that although these states are not minimum-uncertainty states they give the exact classical motion. As an application, it is shown that these coherent states can be used to facilitate the derivation, in the semi-classical limit, of the equations of fluid dynamics in a rotating frame corresponding to a nucleon in a rotating nucleus.