Effect of Medium Viscosity on Some Quantum Systems

Abstract

Particles that are moving within a bulk matter are affected by the surrounding atoms. This effect can be recognized by treating matter as a viscous medium. The expression of energy loss by particle in viscous medium was derived by relating it to the orbital angular momentum. This energy expression is used to find a new quantum law that accounts for the effect of viscosity. It was found that this equation is reduced to ordinary Schrödinger equation in the absence of friction. The solution of this equation shows that both energy and viscosity coefficient are quantized and are related to the orbital quantum number. The total energy reduces to that of ordinary one in the absence of viscosity. The Renod's number agrees with the known one. In this work the kinetic and potential energy, beside the viscous energy for harmonic oscillator and their relation to each other was found. The expression of viscous energy was simplified by relating the classical and quantum expressions according to correspondence principle. This viscous energy expression was added to the classical Hamiltonian energy to find the total medium energy. This total energy beside the wave equation of wave packet was used to find the modified Schrödinger equation.