QUANTUM ANALYSIS OF THE DAMPED HARMONIC-OSCILLATOR AND ITS UNITARY TRANSFORMED SYSTEMS

The damped harmonic oscillator (DHO) and its two unitary transformed s ystems are analyzed both classically and quantum mechanically. To obta in the Hamiltonians of the two canonically transformed systems from th at of the damped harmonic oscillator, we used the displacement operato r and the squeeze operator as the generators of the unitary transforma tions of the canonical coordinates and their conjugate momenta. For th e DHO and its two transformed systems, we evaluated the Schrodinger so lutions and the uncertainties of the position and the momentum operato rs with the uncertainty relations. It was shown that as a result of th e unitary transformation, the classical Hamiltonian of DRO transformed by a squeeze operator was one of the Hamiltonians of a damped harmoni c oscillator.