Generalized approach to applications of quantum time-dependent harmonic oscillator model with variable mass and frequency via dynamical invariant formalism
Pramana - Journal of Physics, vol.100, no.3, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 100 Issue: 3
- Publication Date: 2026
- Doi Number: 10.1007/s12043-026-03155-y
- Journal Name: Pramana - Journal of Physics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Compendex, INSPEC, Academic Search Ultimate (EBSCO), Engineering Source (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Keywords: 02.90.+p, 03.65.-w, 03.65.Ca, 03.65.Fd, dynamical invariance formalism, invariant operator, Pinney’s equation, Time-dependent harmonic oscillator
- Middle East Technical University Affiliated: Yes
Abstract
This article offers complete analytical solutions to the one-dimensional time-dependent Schrödinger equation for an explicit frequency-dependent factor with time-varying mass and frequency by implementing the Lewis-Riesenfeld (LR) dynamical invariance procedure. The present approach proposes a dynamically quantum-invariant phase factor for the wave function of the time-dependent harmonic oscillator model. In this context, a time-dependent system is often transformed into a time-independent one via an integral of motion under appropriate unitary transformations. Various cases of oscillatory systems involving time-dependent mass and frequency forms are also examined algebraically. As a result, the corresponding analytical solutions of the Pinney equation can be employed in nonlinear configuration analyses of such systems.