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

Journal of Quantum Information Science

Coherent States and Uncertainty Product of the Harmonic Oscillator with Position-Dependent Mass

Chadia Qotni, Hicham Laribou

Published Jan 1, 2022• 0 citations
Publisher

Abstract

In this work, we applied the invariant method to calculate the coherent state of the harmonic oscillator with position-dependent mass, which in modern physics has great application. We also obtain the calculation of Heisenberg’s uncertainty principle, and we will show that it is verified.
DOI
10.4236/jqis.2022.121002

Related papers

New coherent states with applications to time-dependent systems

A. K. Rajagopal, John T. Marshall

A new class of coherent states is defined, having all the properties of the usual coherent states except that the uncertainty product of position and momentum need not be minimum. From the stationary-action principle, the dynamical equations of motion for the expectation values and uncertainties for position and momentum are deduced. For the time-dependent harmonic oscillator, the equation for the uncertainty in the position is found to be the well-known Lewis constraint.

Physical Review A•Nov 1, 1982•60 citations

Harmonic Oscillators, Heisenberg's Uncertainty Principle and Simultaneous Measurement Precision for Position and Momentum

Donald Jack Kouri

At the recent QSCP XIX, the author claimed a procedure of using a scaled Fourier transform (the scaling being determined by the detailed interaction and particle mass for a harmonic oscillator) to achieve simultaneous resolution of position and momentum greater than the standard Heisenberg value of 1/2. The procedure is, in fact, invalid for quantum mechanics. The purpose of this paper is simply to give the correct analysis of the uncertainty product, thereby clarifying the error made.

arXiv:1409.2468•Sep 8, 2014•4 citations

Quantum theory of a non-Hermitian time-dependent forced harmonic oscillator having 𝒫𝒯 symmetry

I. A. Pedrosa, B. F. Ramos, K. Bakke +1 more

We discuss the quantum theory of an harmonic oscillator with time-dependent mass and frequency submitted to action of a complex time-dependent linear potential with [Formula: see text] symmetry. Combining the Lewis and Riesenfeld approach to time-dependent non-Hermitian Hamiltonians having [Formula: see text] symmetry and linear invariants, we solve the time-dependent Schrödinger equation for this problem and use the corresponding quantum states to construct a Gaussian wave packet solution. We show that the shape of this wave packet does not depend on the driving force. Afterwards, using this wave packet state, we calculate the expectation values of the position and momentum, their fluctuations and the associated uncertainty product. We find that these expectation values are complex numbers and as a consequence the position and momentum operators are not physical observables and the uncertainty product is physically unacceptable.

International Journal of Modern Physics A•Oct 30, 2019•7 citations

Exact lower bound of the uncertainty principle product for the harmonic oscillator with position-momentum coupling

Yamen Hamdouni

We show that the uncertainty principle product for the position and momentum operators for a system described by the Hamiltonian $ \hat H= \frac{\hat{p}^2}{2m} +\frac{1}{2} m ω^2 \hat{x}^2+\fracμ{2}(\hat x \hat p+ \hat p \hat x)$ where $μ<ω$ reads $Δx Δp\ge\frac{\hbar ω}{2\sqrt{ω^2-μ^2}}$. All the values bellow this lower bound are thus quantum-mechanically forbidden. We construct the annihilation and creation operators for this system and we calculate the expectation values of the operators $\hat p$ and $\hat x$ with respect to the corresponding coherent states.

arXiv:2402.07842•Feb 12, 2024•0 citations

Harmonic oscillator with time-dependent mass and frequency and a perturbative potential

CELIA M. A. DANTAS, I. A. Pedrosa, B. Baseia

A general treatment of the quantized harmonic oscillator with time-dependent mass and frequency is presented. The treatment is also applied to the time-dependent oscillator under the action of a time-dependent perturbative potential. The treatment is based on the use of some time-dependent transformations and in the method of invariants of Lewis and Riesenfeld [J. Math. Phys. 10, 1458 (1969)]. Exact coherent states for such systems are also constructed.

Physical Review A•Feb 1, 1992•107 citations

Exact wave functions of a harmonic oscillator with time-dependent mass and frequency

I. A. Pedrosa

We use the Lewis and Riesenfeld invariant method [J. Math. Phys. 10, 1458 (1969)] to obtain the exact Schr\"odinger wave functions for a harmonic oscillator with time-dependent mass and frequency. Exact coherent states for such system are also constructed.

Physical Review A•Apr 1, 1997•189 citations
We discuss the quantum theory of an harmonic oscillator with time-dependent mass and frequency submitted to action of a complex time-dependent linear potential with [Formula: see text] symmetry. Combining the Lewis and Riesenfeld approach to time-dependent non-Hermitian Hamiltonians having [Formula: see text] symmetry and linear invariants, we solve the time-dependent Schrödinger equation for this problem and use the corresponding quantum states to construct a Gaussian wave packet solution. We show that the shape of this wave packet does not depend on the driving force. Afterwards, using this wave packet state, we calculate the expectation values of the position and momentum, their fluctuations and the associated uncertainty product. We find that these expectation values are complex numbers and as a consequence the position and momentum operators are not physical observables and the uncertainty product is physically unacceptable.
We show that the uncertainty principle product for the position and momentum operators for a system described by the Hamiltonian $ \hat H= \frac{\hat{p}^2}{2m} +\frac{1}{2} m ω^2 \hat{x}^2+\fracμ{2}(\hat x \hat p+ \hat p \hat x)$ where μ<ωμ<ωμ<ω reads ΔxΔp≥ℏω2ω2−μ2Δx Δp\ge\frac{\hbar ω}{2\sqrt{ω^2-μ^2}}ΔxΔp≥2ω2−μ2​ℏω​. All the values bellow this lower bound are thus quantum-mechanically forbidden. We construct the annihilation and creation operators for this system and we calculate the expectation values of the operators p^\hat pp^​ and x^\hat xx^ with respect to the corresponding coherent states.