Journal ArticleDOI
Is there any unique frequency operator for quantum-mechanical anharmonic oscillators
TLDR
In this article, the authors show that the apparent differences between the frequency operators derived by different approaches are due to the different ordering of noncommuting observables and derive some relations between the existing frequency operators.About:
This article is published in Physics Letters A.The article was published on 2005-06-27. It has received 10 citations till now. The article focuses on the topics: Operator (computer programming) & Observable.read more
Citations
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Journal ArticleDOI
Control of higher order antibunching
TL;DR: In this paper, the authors derived a new general criterion for higher order antibunching, based on general physical arguments, which increases with the order of antibunched photon states.
Journal ArticleDOI
Quantum anharmonic oscillator plus delta-function potential: a molecular view of pairing formation and breaking in the coordinate space
Journal ArticleDOI
Energy transfer to an anharmonic diatomic system
José Récamier,W. Luis Mochán +1 more
TL;DR: In this paper, an anharmonic diatomic molecule was modeled using deformed creation and annihilation operators such that the energy spectrum generated by a Hamiltonian of the harmonic oscillator's form written in terms of deformed operators is similar to that of a Morse potential.
Journal ArticleDOI
Secular Terms in Dyson Series to All-Orders of Perturbation
TL;DR: In this paper, it was shown that in a generic quantum mechanical system, the Dyson series can be systematically removed to all orders of perturbation by the method of improved (renormalized) perturbations.
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Generalised quantum anharmonic oscillator using an operator ordering approach
TL;DR: In this paper, a generalised expression for the normal ordering of (a+a^{\dagger})^{m} for integral values of m was constructed and used to study the quantum anharmonic oscillator problem in the Heisenberg approach.
References
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Book
Advanced mathematical methods for scientists and engineers
Carl M. Bender,Steven A. Orszag +1 more
TL;DR: A self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference equations is given in this paper.
Book
Introduction to perturbation techniques
TL;DR: In this paper, the authors introduce the notion of forced Oscillations of the Duffing Equation and the Mathieu Equation for weakly nonlinear systems with quadratic and cubic nonlinearities.
Book
Introduction to Perturbation Theory in Quantum Mechanics
TL;DR: PERTURBATION Theory in QUANTUM MECHANICS Bound States Equations of Motion Examples Perturbation theory in the COORDINATE REPRESENTATION The method of Dalgarno and Stewart Logarithmic Perturbation Theory The Method of Fernandez and Castro PERTURbation theory without WAVE-FUNCTION Hypervirial and Hellmann-Feynman Theorems The Method for Swenson and Danforth Moment Method PERTurbation Theory in Operator Form SIMPLE ATOMIC and MOLEC
Journal ArticleDOI
Multiple-Scale Analysis of the Quantum Anharmonic Oscillator
TL;DR: Multiple-scale analysis of the Heisenberg operator equations of motion for the quantum anharmonic oscillator yields a system of nonlinear operator differential equations, which is solved exactly and provides an operator mass renormalization of the theory.
Journal ArticleDOI
Multiple-Scale Analysis of Quantum Systems
TL;DR: Multiple-scale perturbation theory is extended to study the Heisenberg operator equations of motion and the Schrodinger equation for the quantum anharmonic oscillator to clarify the connection between weak-coupling perturbative and semiclassical nonperturbative aspects of the wave function.