QUANTUM-MECHANICAL TREATMENT OF THE GENERAL DAMPED HARMONIC-OSCILLATOR

A large number of Hamiltonians associated with the canonical variables correspond to the same classical equation of motion. For the general damped harmonic oscillator, we have derived the wave functions for eac h Hamiltonian by the use of the invariant operator method. The quantum averages of the canonical momentum have different form for each Hamil tonian, while those of the kinetic momentum (simple product of mass an d velocity) are equivalent for all Hamiltonians with the same classica l equation of motion. In a concrete form, we have evaluated the quantu m averages and the uncertainty relations for two Hamiltonians.