Relating Classical and Quantum Descriptions of the Damped Harmonic Oscillator

The classical damped harmonic oscillator is a common problem studied in the undergraduate curriculum. The quantum version, however, is almost never discussed. In this work, we show how to relate the classical and quantum descriptions of the damped harmonic oscillator for use in an undergraduate (or graduate) quantum mechanics course. Treating this material also allows for a discussion of decoherence and dissipation, which often is not covered in quantum classes, but is an important element in quantum information science and needs to be included as we modernize the quantum-mechanics curriculum.