  We consider two quantization approaches to the Bateman oscillator model. One
is Feshbach-Tikochinsky's quantization approach reformulated concisely without
invoking the ${\mathit{SU}(1,1)}$ Lie algebra, and the other is the
imaginary-scaling quantization approach developed originally for the
Pais-Uhlenbeck oscillator model. The latter approach overcomes the problem of
unbounded-below energy spectrum that is encountered in the former approach. In
both the approaches, the positive-definiteness of the squared-norms of the
Hamiltonian eigenvectors is ensured. Unlike Feshbach-Tikochinsky's quantization
approach, the imaginary-scaling quantization approach allows to have stable
states in addition to decaying and growing states.
