Schrodinger Equation for Particle with Friction
Alexios P. Polychronakos, Rodanthy Tzani
Abstract
A new quantum mechanical wave equation describing a particle with frictional forces is derived. It depends on a parameter α whose range is determined by the coefficient of friction γ, that is, 0 ≤ α≤ γ. For one extreme value of this parameter, α= 0, we recover Kostin's equation. For the other extreme value, α= γ, 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 β, as well as localized stationary states in the absence of external potentials. Other physical properties of this new class of equations are also discussed.
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