Schrodinger Equation for Particle with Friction

TL;DR

This paper introduces a novel quantum wave equation for particles with friction, incorporating a parameter that interpolates between known equations and reveals new physical phenomena like symmetry breaking and localized states.

Contribution

It derives a new quantum equation for particles with friction, unifying and extending previous models, and explores its physical implications and properties.

Findings

Recover Kostin's equation at one extreme of the parameter

Identify friction effects manifesting as magnetic-like terms

Discover localized stationary states without external potentials

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, $0 \leq \alpha \leq \gamma$. 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.