A RADIATIVE MODEL OF QUANTIZATION OF AN OSCILLATOR WITH DISSIPATION

For an example of friction forces directly proportional to the velocit y of motion, a new approach is proposed to the problem of quantization of systems with energy dissipation. An analogy with the radiative fri ction forces of Lorentz is widely used. The power of dissipation force s is expanded in harmonic components and, by using the correspondence principle, recalculated into the rate of change of the population prob ability of an excited state. Quantum dynamics is described by the temp oral Green functions in the Feynman integral representation. In the ca se of a harmonic oscillator, analytic expressions for temporal behavio r of the probability amplitudes are derived, and the entire spectrum o f complex energies is obtained. Their imaginary part gives a quantitat ive description of the energy dissipation. In our scheme, the ground s tate is found to be stable.