The Harmonic Potential Theorem for a Quantum System with Time-Dependent Effective Mass

Omar Gamel, Daniel F. V. James, Timothy C. Ralph +1 more

Meng-Yun Lai, Duan-Liang Xiao, Xiao‐Yin Pan

We investigate the many-body wave function of a quantum system with time-dependent effective mass, confined by a harmonic potential with time-dependent frequency, and perturbed by a time-dependent spatially homogeneous electric field. It is found that the wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. The wave function reduces to that of the harmonic potential theorem wave function when both the effective mass and frequency are static. An example of application is also given.

Meng-Yun Lai, Xiao‐Yin Pan

We investigate the evolution of the many-body wave function of a quantum system with time-varying effective mass, confined by a harmonic potential with time-varying frequency in the presence of a uniform time-varying magnetic field, and perturbed by a time-dependent uniform electric field. It is found that the wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. In other words, we generalize the harmonic potential theorem to the case when the effective mass, harmonic potential, and the external uniform magnetic field with arbitrary orientation are all time-varying. The results reduce to various special cases obtained in the literature, particulary to that of the harmonic potential theorem wave function when the effective mass and frequency are both static and the external magnetic field is absent.

Farhad H. M. Faisal

Giovanni Vignale

It is shown that the theorem asserting separability of the center of mass motion for a system of interacting particles in a harmonic external potential is satisfied in the time dependent density functional theory, provided that the exchange-correlation potential satisfies a simple symmetry under transformation to an accelerated frame of reference. Examples of approximations for the exchange-correlation potential which satisfy or violate this symmetry are given.

Chao‐Yun Long, Shuijie Qin, Zhu-Hua Yang +1 more