Quantum harmonic oscillator with time-dependent mass and frequency

The quantum harmonic oscillator with time-dependent mass and frequency is analyzed by using the canonical transformation method. The varying mass and frequency of the system are reduced to constant mass and frequency, and the corresponding eigenvalues and eigenvectors are derived. The exact time-dependent coherent state of the harmonic oscillator is constructed and shown to be equivalent to the squeezed state. Damped harmonic oscillators with different frictions and forced time-dependent harmonic oscillators are also discussed.