Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The Harmonic Oscillator, a Review of Classicaland Elementary Quantum Mechanics

Carl W David

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

The classical harmonic oscillator and an elementary discussion of the quantum mechanical solutions for the harmonic oscillator are discussed.

Related papers

The Harmonic Oscillator, The Ladder Operator Solutions

Carl W David

The ladder operator approach to the quantum mechanics of the simple harmonic oscillator is presented.

•Jan 1, 2006•0 citations

From harmonic to anharmonic oscillators

FRANCESCO IACHELLO

The algebraic approach to quantum mechanics is briefly reviewed. The role of oscillator realizations is discussed. Applications to vibrations of complex molecules are presented.

•Jan 1, 1993•0 citations

Integral equations and the simple harmonic oscillator

Gerardo Muñoz

The energy eigenstates for the simple harmonic oscillator in quantum mechanics are found through the solution of an integral equation.

American Journal of Physics•Mar 1, 1998•12 citations

Quantum solutions of the damped harmonic oscillator

Gerard J Milburn, Daniel F. Walls

Solutions to the Fokker–Planck equation for a damped harmonic oscillator corresponding to uniquely quantum-mechanical initial states with no classical correspondence are given.

American Journal of Physics•Dec 1, 1983•33 citations

Quantum, classical and semiclassical momentum distributions: I. Theory and elementary examples

H. J. Korsch, B Schellhaaß

We discuss the basic properties of momentum distributions in quantum mechanics for elementary systems as well as their classical analogue. Semiclassical approximations can show a quantitative connection between the classical and quantum cases. We believe that such distributions provide a useful tool to improve the understanding of elementary quantum mechanics. Important differences between distributions in coordinate and momentum space are pointed out. Elementary examples (free and uniformly accelerating particle, harmonic oscillator and square-well potential) are discussed.

European Journal of Physics•Jan 1, 2000•11 citations

Quantum mechanics and elements of quantum field theory

Rodolfo Gambini, Jorge A. Pullin

This chapter reviews elementary quantum mechanics, the introduction of a Hilbert space, quantum operators, and the promotion of Poisson brackets to commutators. It discusses the Harmonic oscillator, and introduces the number representation and creation and annihilation operators. The chapter then describes some elements of quantum field theory. It focuses on the free Klein-Gordon field as an example and shows that it can be viewed as a collection of Harmonic oscillators. The chapter then covers interacting quantum field theories, the interaction picture, Wick's theorem, and Feynman diagrams, and briefly considers renormalizability, the problems that arise in the case of gravity, and the asymptotic safety scenario.

Oxford University Press eBooks•Sep 22, 2011•0 citations
We discuss the basic properties of momentum distributions in quantum mechanics for elementary systems as well as their classical analogue. Semiclassical approximations can show a quantitative connection between the classical and quantum cases. We believe that such distributions provide a useful tool to improve the understanding of elementary quantum mechanics. Important differences between distributions in coordinate and momentum space are pointed out. Elementary examples (free and uniformly accelerating particle, harmonic oscillator and square-well potential) are discussed.
This chapter reviews elementary quantum mechanics, the introduction of a Hilbert space, quantum operators, and the promotion of Poisson brackets to commutators. It discusses the Harmonic oscillator, and introduces the number representation and creation and annihilation operators. The chapter then describes some elements of quantum field theory. It focuses on the free Klein-Gordon field as an example and shows that it can be viewed as a collection of Harmonic oscillators. The chapter then covers interacting quantum field theories, the interaction picture, Wick's theorem, and Feynman diagrams, and briefly considers renormalizability, the problems that arise in the case of gravity, and the asymptotic safety scenario.