Schrodinger Equation for Particle with Friction

Abstract

A new quantum mechanical wave equation describing a particle with frictional forces is derived. It depends on a parameter $\alpha$ whose range is determined by the coefficient of friction $\gamma$, that is, $0\le \alpha \le \gamma$. For one extreme value of this parameter, $\alpha =0$, we recover Kostin's equation. For the other extreme value, $\alpha =\gamma$, we obtain an equation in which friction manifests in "magnetic" type terms. It further exhibits breakdown of translational invariance, manifesting through a symmetry breaking parameter $\beta$, as well as localized stationary states in the absence of external potentials. Other physical properties of this new class of equations are also discussed.

11 pages