  The motivation of this work is to get an additional insight into the
irreversible energy dissipation on the quantum level. The presented examination
procedure is based on the Feynman path integral method that is applied and
widened towards the calculation of the kernel of a quantum mechanical damped
oscillator. Here, it is shown that the energy loss of the oscillator can be
generated by the introduced harmonic complex potential. The related damped wave
function, however, does not pertain to the probability meaning as it is usual
in the case of complex absorbing potentials. This decrease of the wave function
is evaluated, moreover, the energy dissipation and the measure the
irreversibility are expressed.
