Abstract:
Method of quantum description of dissipative systems based on the classical
approach using friction forces is proposed. A Hamiltonian is obtained for motion with
friction. The method is applied to the description of a linear oscillator with friction.
The operator equations of motion are solved for this case. The motion integral connected
with the energy conservation law and the form of the corresponding operator, its eigenvalues
and eigenfunctions are found. The exact solutions of the Schrodinger equation is
obtained and the correspondence with the classical problem is investigated.