Microscopic derivation of a frictional Schrödinger equation

Alexios P. Polychronakos, Rodanthy Tzani

Nicolas Gisin

Ebtisam A. Mohamed, Mubarak Dirar, Ibrahim Adam Ibrahim Hammad +2 more

By treating particles as harmonic oscillator is obtained the friction energy related to the momentum. The energy and the corresponding Newtonian operator is found. This result in a new Schrodinger equation accounting for the effect of friction. This new equation shows that the energy and mass are quantized, if one treats particles as strings. The radioactive decay law and collision probability is also derived.

Morton D. Kostin

It is shown that the Heisenberg-Langevin equation can be used to derive a Schrödinger equation for a Brownian particle interacting with a thermal environment. The equation derived is iℏ(∂ψ/∂ t)=−(ℏ2/2m)∇2ψ+Vψ+VRψ+[(ℏ f/2im) ln(ψ/ψ*)+W(t)]ψ(r, t), W(t)=−(ℏ f/2im)∫ψ* ln(ψ/ψ*)ψ dr,where f is the friction constant and VR is a random potential.

H. N. Ioannidou

Somnath Pal

The damped harmonic oscillator is used to represent the damping processes in nature. Therefore it is necessary to find the Hamiltonian for the damped oscillator. The Hamiltonian is developed for the harmonic oscillator with frictional force proportional to velocity. The solution of the Schr\"odinger equation gives nonstationary states. The quantum friction coefficient is derived to be zero for massless particles. It is thought that velocity-dependent forces exist near the nucleus and therefore, the scattering amplitude for the deep inelastic process is derived.