Exact evolution of the generalized damped harmonic oscillator

Information theories for time-dependent harmonic oscillator

“…Stimulated by these recent trends, we are going to analyze in this work the informational entropy and its relevant quantum measures for the time-dependent harmonic oscillator by making use of the invariant operator theory [3,[20][21][22][23][24][25][26][27]. The invariant operator theory of the time-dependent harmonic oscillator is based on the construction of adiabatic invariants which was firstly introduced by Lewis and Riesenfeld [21] in describing its quantum features.…”

Davydov–Chaban Hamiltonian in presence of time-dependent potential

“…Study of timedependent interaction of quantum mechanical systems provides fundamental structure of basic physics and interpretation of new physics in different areas of physics, such as, gravitation [17], quantum optics [18,19], the Paul trap [20][21][22] and spintronics [23]. To study time-dependent systems remarkable efforts have been made to get an analytical solution of the time-dependent Hamiltonians [24][25][26][27][28][29] using different methods for instance, path integral, second quantization and dynamical invariant.…”

Study of Time Evolution for Approximation of Two-Body Spinless Salpeter Equation in Presence of Time-Dependent Interaction

“…In most cases, the exact analytical techniques fail and we have to use approximate methods for our real physical problems. Till now, a variety of techniques have been applied to the field including the path integral [20], dynamical invariant [21][22][23], and Gaussian wave packet [24]. Albeverio and Mazzucchi considered Schrödinger equation with a time-dependent quadratic plus quartic Hamiltonian and using Feynman path integral representation [25].…”