Electron behavior in hydrogen atom under electric fields

Polarization, charge transport, breakdown, space charge and other electrical phenomena have been studied under a quantum level. Several theories and codes based on Schrodinger equation have been applied. However, there are inevitable defects in these methods, e.g. excessive simplification, which is not reasonable when studying electrical phenomena. This paper is to study electron behavior under electric fields under a quantum level and with as less simplification as possible. A simple case is studied, where only one hydrogen atom is bounded in a limited space with a uniform electric field. Based on Schrodinger equation, mathematical model is built. The model is a partial differential equation and analytical solution is not available. Finite difference method (FDM) is employed to solve time-independent problem and introduces an error. The error decreases when using a finer meshing. Modified Euler method (MEM) is adopted to solve time-dependent equation and introduces a similar error. All these errors are estimated and limited within a reasonable range. By studying the one Hydrogen atom case, electronic polarization is predicted. Polarization intensity under different additional electric field is calculated. Polarization speed, namely response, is calculated by solving time-dependent equation, which is usually unavailable by conventional methods. We expect the application under more complex conditions and to predict more electrical phenomena.