The wave function of an electron in a time varying electric field, a static magnetic field and a impurity potential can be transformed to the wave function of an electron without the electric field. By a unitary transformation, the electric field can be rigorously eliminated.
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.
We calculated near-threshold photodetachment cross sections for ${\mathrm{Cs}}^{\ensuremath{-}}$ in the presence of a dc electric field using three different approaches: the frame-transformation method with and without rescattering effects and the Kirchhoff-integral approach. Radial wave functions for the electronic motion were obtained using the Pauli equation method with a model potential describing the effective electron-atom interaction. Our results demonstrate the inadequacy of the frame-transformation method in the 3P resonance region even for weak fields (E<10kV/cm). We show that the triplet and singlet contributions to the total cross section can be manipulated by varying the external electric field. This can enhance spin-orbit effects in the photodetachment process and create more favorable conditions in the experiment for the observation of the lowest 3P resonance in ${\mathrm{Cs}}^{\ensuremath{-}}.$
The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the system, whereas unitary transformation approach is used when managing the system in the framework of quantum mechanics. For both approaches, the original system is transformed to a much more simple system that is the sum of two independent harmonic oscillators which have time-dependent frequencies. We therefore easily identified the wave functions in the transformed system with the help of invariant operator of the system. The full wave functions in the original system is derived from the inverse unitary transformation of the wave functions associated to the transformed system.