An exact solution for electrons in a time-dependent magnetic field

Bin Chen

As is well known, the phase changes with electron transport in the time-evolution magnetic field. In this paper, with evolution operator in tow-level systems, we obtain several exact solutions. Then we analyze their phase. By the time-dependent Schrdinger equation, we obtain dynamical phase, and then we have Aharonov-Anandan phase. At last, we compare them with Berry phase.

M. Taut

LIANGMai-Lin, LIULi-Yan

In cylindrical coordinate, exact wave functions of the two-dimensional time-dependent harmonic oscillator in a time-dependent magnetic field are derived by using the trial function method. Meanwhile, the exact classical solution as well as the classicalphase is obtained too. Through the Heisenberg correspondence principle, the quantum solution and the classical solution are connected together.

Wenhua Huang, Jingyan Mao, W.G. Qiu

A generalized G G -expansion method is extended to construct exact solutions for the Gross-Pitaevskii equation with weak bias magnetic and time-dependent laser fields.Many types of exact solutions including hyperbolic function solution, trigonometric function solution and rational exact solution with parameters are obtained.In addition, soliton solutions are found.

Shi‐Hai Dong