Damping Effect of Electromagnetic Radiation and Time-Dependent Schrodinger Equation

Abstract

The inexactness of the time-dependent Schr\"odinger equation of a charged particle in an external electromagnetic field is discussed in terms of the damping effect of the radiation. A possible improvement is to add a nonlinear term representing this effect to the linear Schr\"odinger equation. Conditions for the nonlinear term are investigated and it is demonstrated that the obtained nonlinear Schr\"odinger equation may present state evolutions similar to the wave-function reduction and transitions between stationary states.