Quantum Damped Harmonic Oscillator Revisited

Mario Cesar Baldiotti, R. Fresneda, Dmitri M Gitman

A. L. De Brito, Fabio Cabral Carvalho, B. Baseia +1 more

Pintu Bhattachary, Ravi Ranjan

We display some important definitions of q-calculus along with some essential formulae of q-Laplace transform. Then, we apply them to realize the locomotion of a damped harmonic oscillator for over-damped, under damped, and critically damped situation. Thus, the mathematical statement of motion of a damped harmonic oscillator (DHO) is revisited and reviewed in view of quantum calculus. The dimensionality of all the parameters associated to the problem are discussed to find exact solutions. It is also found that, as q tends to 1, the solution takes the form as it is in classical Leibnitz calculus.

Chung‐In Um, Kyu-Hwang Yeon, Thomas F. George

Caixa Postal

We return to the description of the damped harmonic oscillator by means of a closed quantum theory with a general assessment of previous works, in particular the Bateman-CaldirolaKanai model and a new model recently proposed by one of the authors. We show the local equivalence between the two models and argue that latter has better high energy behavior and is naturally connected to existing open-quantum-systems approaches.

Hermann Grabert, Ulrich Weiß, Peter Talkner A