Quantization of the damped harmonic oscillator based on a modified Bateman Lagrangian
arXiv:2002.05435 · doi:10.1103/PhysRevA.101.022105
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 (14)
- The classical mechanics of non-conservative systems
- Open quantum systems
- Quantum damped oscillator I: dissipation and resonances
- A Canonical Approach to the Quantization of the Damped Harmonic Oscillator
- Quantization of the Damped Harmonic Oscillator Revisited
- QUANTUM DISSIPATION AND QUANTUM NOISE
- Bateman's dual system revisited: I. Quantization, geometric phase and relation with the ground-state energy of the linear harmonic oscillator
- Two quantization approaches to the Bateman oscillator model
- The principle of stationary nonconservative action for classical mechanics and field theories
- Classical and quantum effective theories
- Quantum damped oscillator II: Bateman's Hamiltonian vs. 2D Parabolic Potential Barrier
- Connecting dissipation and noncommutativity: A Bateman system case study
- Symmetries of the quantum damped harmonic oscillator
- Relativistic Lagrangians for the Lorentz-Dirac equation
Cited by in corpus (6)
- Quadratic Time-dependent Quantum Harmonic Oscillator
- A new approach to the quantization of the damped harmonic oscillator
- Quantization of nonlinear non-Hamiltonian systems
- Classical Hamiltonian Systems with Balanced loss and gain
- The quantum harmonic oscillator and the real Hilbert space
- Identical damped harmonic oscillators described by coherent states