It is well known that to quantize any dynamical system it isnecessaryfor a generator of the classical motion to exist in the form of a Hamiltonian function. It is shown, by using the example of a damped harmonic oscillator, that a particular class of inequivalent classical Hamiltonians exist which make quantization of the system ambiguous. Hence it is conclued that it isnotsufficientfor the Hamiltonian to merely generate the motion, but it must also be necessarily related via a canonical transformation to the total energy of the system.