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.

To solve this equation using the Lagrange method, we first define the Lagrangian of the system: L = T - V where T is the kinetic energy of the system and V is the potential energy of the system. For a ...

The harmonic oscillator with time-dependent (indefinite and variable) mass subject to the force proportional to velocity is studied by extending Bateman’s dual Lagrangian and Hamiltonian formalism. To ...

The results of fractional calculus reduce to those obtained from classical calculus (the standard Euler Lagrange equations) when γ→0 and α, β are equal unity only. ... The Hamiltonian and Lagrangian ...

This article explains and illustrates the use of a set of coupled dynamical equations, second order in a fictitious time, which converges to solutions of stationary Schr\"{o}dinger equations with ...

The quantum theory of damping is presented and illustrated by means of a driven damped harmonic oscillator. The theory is formulated in the coherent state representation which illustrates very vividly ...