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

arXiv:1006.3352 · International Journal of Theoretical Physics

On Close Relationship Between Classical Time-Dependent Harmonic Oscillator and Non-relativistic Quantum Mechanics in One Dimension

Alexander Davydov

Published Jan 7, 2011• 9 citations
arXivHTMLPDF
DOI
10.1007/s10773-010-0654-1

Related papers

On the exactness of the semi-classical approximation for non-relativistic one-dimensional propagators

I Semiz, K Düztaş

For one-dimensional non-relativistic quantum mechanical problems, we investigate the conditions for all the position dependence of the propagator to be in its phase, that is, for the semi-classical approximation to be exact. For velocity-independent potentials we find that: (i) the potential must be quadratic in space, but can have arbitrary time dependence, (ii) the phase may be made proportional to the classical action, and the magnitude (‘fluctuation factor’) can also be found from the classical solution and (iii) for the driven harmonic oscillator the fluctuation factor is independent of the driving term.

arXiv:quant-ph/0608211•Journal of Physics A Mathematical and General•Nov 8, 2006•0 citations

The time-dependent quantum harmonic oscillator revisited: Applications to quantum field theory

Daniel Gómez Vergel, Eduardo J. S. Villaseñor

arXiv:0903.0289•Annals of Physics•Mar 26, 2009•37 citations

Harmonic oscillators in relativistic quantum mechanics

Jacek Karwowski, Grzegorz Pestka

Theoretical Chemistry Accounts•Jun 16, 2007•17 citations

On the exactness of the Semi-Classical Approximation for Non-Relativistic One Dimensional Propagators

İbrahim Semiz, Koray Düztaş

For one dimensional non-relativistic quantum mechanical problems, we investigate the conditions for all the position dependence of the propagator to be in its phase, that is, the semi-classical approximation to be exact. For velocity independent potentials we find that: (i) the potential must be quadratic in space, but can have arbitrary time dependence. (ii) the phase may be made proportional to the classical action, and the magnitude (``fluctuation factor'') can also be found from the classical solution. (iii) for the driven harmonic oscillator the fluctuation factor is independent of the driving term.

•Aug 28, 2006•0 citations

Supersymmetric Dirac Hamiltonians in ($$1+1$$) dimensions revisited

Georg Junker

Abstract The most general Dirac Hamiltonians in $$(1+1)$$ ( 1 + 1 ) dimensions are revisited under the requirement to exhibit a supersymmetric structure. It is found that supersymmetry allows either for a scalar or a pseudo-scalar potential. Their spectral properties are shown to be represented by those of the associated non-relativistic Witten model. The general discussion is extended to include the corresponding relativistic and non-relativistic resolvents. As example, the well-studied relativistic Dirac oscillator is considered and the associated resolved kernel is found in a closed-form expression by utilising the energy-dependent Green’s function of the non-relativistic harmonic oscillator. The supersymmetric quasi-classical approximation for the Witten model is extended to the associated relativistic model.

arXiv:1911.00454•The European Physical Journal Plus•Jun 1, 2020•17 citations

Classical and quantum harmonic oscillators subject to a time dependent force

Henryk Gzyl

arXiv:2204.03460•Jan 1, 2022•0 citations
For one-dimensional non-relativistic quantum mechanical problems, we investigate the conditions for all the position dependence of the propagator to be in its phase, that is, for the semi-classical approximation to be exact. For velocity-independent potentials we find that: (i) the potential must be quadratic in space, but can have arbitrary time dependence, (ii) the phase may be made proportional to the classical action, and the magnitude (‘fluctuation factor’) can also be found from the classical solution and (iii) for the driven harmonic oscillator the fluctuation factor is independent of the driving term.
For one dimensional non-relativistic quantum mechanical problems, we investigate the conditions for all the position dependence of the propagator to be in its phase, that is, the semi-classical approximation to be exact. For velocity independent potentials we find that: (i) the potential must be quadratic in space, but can have arbitrary time dependence. (ii) the phase may be made proportional to the classical action, and the magnitude (``fluctuation factor'') can also be found from the classical solution. (iii) for the driven harmonic oscillator the fluctuation factor is independent of the driving term.
Supersymmetric Dirac Hamiltonians in (1+11+11+1) dimensions revisited
Abstract The most general Dirac Hamiltonians in (1+1)(1+1)(1+1) ( 1 + 1 ) dimensions are revisited under the requirement to exhibit a supersymmetric structure. It is found that supersymmetry allows either for a scalar or a pseudo-scalar potential. Their spectral properties are shown to be represented by those of the associated non-relativistic Witten model. The general discussion is extended to include the corresponding relativistic and non-relativistic resolvents. As example, the well-studied relativistic Dirac oscillator is considered and the associated resolved kernel is found in a closed-form expression by utilising the energy-dependent Green’s function of the non-relativistic harmonic oscillator. The supersymmetric quasi-classical approximation for the Witten model is extended to the associated relativistic model.