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.
