Quantization of the damped harmonic oscillator based on a modified Bateman Lagrangian

Abstract

An approach to quantization of the damped harmonic oscillator (DHO) is developed on the basis of a modified Bateman Lagrangian (MBL); thereby some quantum mechanical aspects of the DHO are clarified. We treat the energy operator for the DHO, in addition to the Hamiltonian operator that is determined from the MBL and corresponds to the total energy of the system. It is demonstrated that the energy eigenvalues of the DHO exponentially decrease with time and that transitions between the energy eigenstates occur in accordance with the Schrödinger equation. Also, it is pointed out that a new critical parameter discriminates different behaviours of transition probabilities.

7 pages, 8 figures

References in corpus (3)

• The principle of stationary nonconservative action for classical mechanics and field theories
• Classical and quantum effective theories
• Relativistic Lagrangians for the Lorentz-Dirac equation