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

Physics Letters A

Path integral for the harmonic oscillator in one dimension with nonzero minimum position uncertainty

Khireddine Nouicer

Published Feb 10, 2006• 17 citations
Publisher
DOI
10.1016/j.physleta.2006.02.001

Related papers

Path Integral Formulation of a Damped Harmonic Oscillator

IMPERIAL COLLEGE PRESS eBooks•Jan 1, 2006•0 citations

Generalized path-integral solution and coherent states of the harmonic oscillator in D -dimensions

Ma Yu-Quan, Jin Zhang, Chen Yong-Kang +1 more

We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time-dependent forced harmonic oscillator in D ( D ⩾ 1) dimensions. The coherent states, defined as the eigenstates of annihilation operator, of the D -dimensional harmonic oscillator are derived. These coherent states correspond to the minimum uncertainty states and the relation between them is investigated.

Chinese Physics•Oct 31, 2005•1 citation

Uncertainty of path integral averages at low temperature

Troy W. Whitfield, John E. Straub

Burghardt, Eicke, and Stolze [J. Chem. Phys. 108, 1562 (1998)] have recently presented analytical results for the coherent state path integral (CSPI) approximation to the harmonic oscillator thermal density matrix in a generalized representation. In this work, the variance of the position and momentum operators for the more common Feynman path integral approximation to the density matrix is examined and compared with the results of the generalized CSPI approximation. Both path integral approaches are found to predict minimum uncertainty states at low enough temperatures. Particular attention is given to estimates of internal energy, which can place limits upon the temperature range over which path integral approximations are valid.

The Journal of Chemical Physics•Oct 15, 2001•4 citations

Path Integral Formulation of a Damped Harmonic Oscillator

WORLD SCIENTIFIC eBooks•Feb 19, 2017•0 citations

Minimum uncertainty wave packet in relativistic quantum mechanics

Yukihisa Nogami, F. Masafumi Toyama

In nonrelativistic quantum mechanics in one dimension a wave packet can be constructed for which the minimum uncertainty relation for position and momentum, ΔxΔp=ℏ/2, holds exactly. The wave function of the wave packet is Gaussian and satisfies the Schrödinger equation for a harmonic oscillator potential. We illustrate a similar situation in relativistic quantum mechanics for the one-dimensional Dirac equation.

American Journal of Physics•Jan 12, 2010•2 citations

Path integral analysis of harmonic oscillators with time-dependent mass

M Sabir, Sundararaman Rajagopalan

Pramana•Sep 1, 1991•11 citations
Burghardt, Eicke, and Stolze [J. Chem. Phys. 108, 1562 (1998)] have recently presented analytical results for the coherent state path integral (CSPI) approximation to the harmonic oscillator thermal density matrix in a generalized representation. In this work, the variance of the position and momentum operators for the more common Feynman path integral approximation to the density matrix is examined and compared with the results of the generalized CSPI approximation. Both path integral approaches are found to predict minimum uncertainty states at low enough temperatures. Particular attention is given to estimates of internal energy, which can place limits upon the temperature range over which path integral approximations are valid.