Time dependence of operators in anharmonic quantum oscillators: Explicit perturbative analysis

DOI10.1063/1.532995zbMath0969.81020OpenAlexW2034735647MaRDI QIDQ4498413

Peter B. Kahn, Yair Zarmi

Publication date: 16 August 2000

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.532995

zbMATH Keywords

anharmonic oscillatorsminimal normal formmethod of normal formsextended time scaleshigh-lying excited statesrenormalized form for the propagatortime dependence of operators

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items (5)

ANALYTICAL SOLUTIONS OF ARBITRARY ORDERS TO THE CLASSICAL AND QUANTUM OSCILLATORS WITH VELOCITY-DEPENDENT QUARTIC ANHARMONICITIES ⋮ Is there any unique frequency operator for quantum-mechanical anharmonic oscillators ⋮ Perturbation theory free from secular terms for the equations of motion of anharmonic oscillators ⋮ Classical and quantum-mechanical observables by perturbation theory ⋮ An intuitive approach to the higher-order solutions for classical and quantum oscillators of quartic anharmonicity

Cites Work

• Reduction of secular error in approximations to harmonic oscillator systems with nonlinear perturbations
• Minimal normal forms in harmonic oscillations with small nonlinear perturbations
• Continuum Limit, Galilean Invariance, and Solitons in the Quantum Equivalent of the Noisy Burgers Equation
• Multiple-Scale Analysis of the Quantum Anharmonic Oscillator

This page was built for publication: Time dependence of operators in anharmonic quantum oscillators: Explicit perturbative analysis