Quantization of the damped harmonic oscillator based on a modified Bateman Lagrangian
Shinichi Deguchi, Yuki Fujiwara
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 Schr\"odinger equation. Also, it is pointed out that a new critical parameter discriminates different behaviors of transition probabilities.
Topics & Concepts
Harmonic oscillatorEigenvalues and eigenvectorsHamiltonian (control theory)Quantization (signal processing)Energy operatorLagrangianOperator (biology)Quantum mechanicsSchrödinger equationMathematicsPhysicsMathematical physicsClassical mechanicsEnergy (signal processing)ChemistryBiochemistryAlgorithmRepressorTranscription factorMathematical optimizationGeneQuantum Mechanics and ApplicationsQuantum Mechanics and Non-Hermitian PhysicsQuantum chaos and dynamical systems