Canonical quantization of the Bateman-Morse-Feshbach damped oscillator (Q1182290)

\textit{H. Bateman} [Phys. Rev. 38, 815--819 (1931; Zbl 0003.01101)] studied the damped harmonic oscillator in classical mechanics and \textit{P. M. Morse} and \textit{H. Feshbach} [Methods of Theoretical Physics, Vol. I, II. New York: McGraw-Hill Book Co. (1953; Zbl 0051.40603)] gave a formal description of this in their well-known book. In the present work the authors study the canonical quantization of Bateman's damped oscillator. They give the spectrum of the Hamiltonian and show that the wavefunctions behave asymptotically as a superposition of damped oscillators with their initial values in an appropriately chosen dense subset of the Hilbert space.