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 Physics A Mathematical and Theoretical

Time evolution of a time-dependent inverted harmonic oscillator in arbitrary dimensions

Guangjie Guo, Zhongzhou Ren, Ju Guo-Xing, Xiaoyong Guo

Published Feb 28, 2012• 1 citation
Publisher

Abstract

The time evolution of a time-dependent inverted harmonic oscillator (TDIHO) of arbitrary dimensions is investigated. Using the algebraic method, we obtain the exact orthogonal basis of solutions of a TDIHO in which the dimensionality d and angular momentum l appear as parameters, and also discuss its properties. With the wavepacket as the initial state, the general expressions of sojourn time of a TDIHO are given. The method is also applied to the inverted Caldirola–Kanai harmonic oscillator. The results show that the sojourn time appears as an increasing function of the dissipation parameter in arbitrary dimensions, but a decreasing function of the dimensionality.

DOI
10.1088/1751-8113/45/11/115301

Related papers

Quantum tunneling effect of a time-dependent inverted harmonic oscillator

Guangjie Guo, Zhongzhou Ren, Ju Guo-Xing +1 more

An algebraic method to solve the time-dependent inverted harmonic oscillator (TDIHO) is proposed, and the analytical expressions of the wavefunctions obtained by this method are suitable for discussion of the quantum tunneling effect. With the Gaussian wave packet as the initial state, the general expressions of transmission and reflection probabilities, and dwell time of TDIHO are obtained. The quantum tunneling effect is further illustrated through two specific cases.

Journal of Physics A Mathematical and Theoretical•Apr 5, 2011•12 citations

Quantum tunneling effect of a driven inverted harmonic oscillator

Guangjie Guo, Zhongzhou Ren, Ju Guo-Xing +1 more

Using the algebraic method, we derive the exact wavefunction of a driven time-dependent inverted harmonic oscillator (TDIHO). With the Gaussian wave-packet as the initial state, the general expressions of the transmission probability and dwell time of the driven TDIHO are obtained. For a weak driving force, the dwell time can be separated into two terms. The first term is for the unperturbed part, and the second one is that from the perturbation, which is the effect from the driving force. Furthermore, with two examples, the effect of the driving force on the dwell time is explicitly indicated in detail.

Journal of Physics A Mathematical and Theoretical•Jun 23, 2011•6 citations

Gaussian wave packet states of a generalized inverted harmonic oscillator with time-dependent mass and frequency

I. A. Pedrosa, Alberes Lopes de Lima, Alexandre M. de M. Carvalho

We derive quantum solutions of a generalized inverted or repulsive harmonic oscillator with arbitrary time-dependent mass and frequency using the quantum invariant method and linear invariants, and write its wave functions in terms of solutions of a second-order ordinary differential equation that describes the amplitude of the damped classical inverted oscillator. Afterwards, we construct Gaussian wave packet solutions and calculate the fluctuations in coordinate and momentum, the associated uncertainty relation, and the quantum correlations between coordinate and momentum. As a particular case, we apply our general development to the generalized inverted Caldirola–Kanai oscillator.

Canadian Journal of Physics•Jan 12, 2015•12 citations

Quantum tunnelling of a damped and driven, inverted harmonic oscillator

Sotirios Baskoutas, A. D. Jannussis, R Mignani

Using the evolution operator method, we derive the exact propagator of the generalized parametric oscillator in its more general form. This result is exploited to obtain the exact wavefunction of a damped and driven, inverted harmonic oscillator of the Caldirola-Kanai type, taking a Gaussian wavepacket as the initial state. We discuss the tunnelling process of such a system. The probability density and the persistence probability are evaluated. The expression for the sojourn time is derived for a small external force, and is the sum of two terms, whose explicit forms are obtained in the case of an extended wavepacket. The first term is an increasing function of the dissipation parameter gamma , whereas the second one is strictly due to the presence of the driving force.

Journal of Physics A Mathematical and General•Dec 7, 1993•17 citations

WAVE FUNCTION OF THE TIME-DEPENDENT INVERTED HARMONIC OSCILLATOR

I. A. Pedrosa, I. Guedes

Time-dependent mass and frequency inverted harmonic oscillator is discussed in light of the Lewis and Reisenfeld invariant method. The wave function is found in terms of the Weber function. As an example, we derive the wave function of the inverted Caldirola-Kanai oscillator.

Modern Physics Letters B•Jul 20, 2002•25 citations

The propagator of the time-dependent forced harmonic oscillator with time-dependent damping

Bin Kang Cheng

By using the Caldirola–Kanai Hamiltonian and by applying Feynman polygonal paths, exact evaluation of the propagator of one-dimensional time-dependent forced and damped harmonic oscillator, based on the work of Montroll in deriving the propagator of the harmonic oscillator with time-dependent frequency, is possible. The results are compared with previously found results.

Journal of Mathematical Physics•Jan 1, 1986•11 citations
The time evolution of a time-dependent inverted harmonic oscillator (TDIHO) of arbitrary dimensions is investigated. Using the algebraic method, we obtain the exact orthogonal basis of solutions of a TDIHO in which the dimensionality d and angular momentum l appear as parameters, and also discuss its properties. With the wavepacket as the initial state, the general expressions of sojourn time of a TDIHO are given. The method is also applied to the inverted Caldirola–Kanai harmonic oscillator. The results show that the sojourn time appears as an increasing function of the dissipation parameter in arbitrary dimensions, but a decreasing function of the dimensionality.
Using the algebraic method, we derive the exact wavefunction of a driven time-dependent inverted harmonic oscillator (TDIHO). With the Gaussian wave-packet as the initial state, the general expressions of the transmission probability and dwell time of the driven TDIHO are obtained. For a weak driving force, the dwell time can be separated into two terms. The first term is for the unperturbed part, and the second one is that from the perturbation, which is the effect from the driving force. Furthermore, with two examples, the effect of the driving force on the dwell time is explicitly indicated in detail.
We derive quantum solutions of a generalized inverted or repulsive harmonic oscillator with arbitrary time-dependent mass and frequency using the quantum invariant method and linear invariants, and write its wave functions in terms of solutions of a second-order ordinary differential equation that describes the amplitude of the damped classical inverted oscillator. Afterwards, we construct Gaussian wave packet solutions and calculate the fluctuations in coordinate and momentum, the associated uncertainty relation, and the quantum correlations between coordinate and momentum. As a particular case, we apply our general development to the generalized inverted Caldirola–Kanai oscillator.
Using the evolution operator method, we derive the exact propagator of the generalized parametric oscillator in its more general form. This result is exploited to obtain the exact wavefunction of a damped and driven, inverted harmonic oscillator of the Caldirola-Kanai type, taking a Gaussian wavepacket as the initial state. We discuss the tunnelling process of such a system. The probability density and the persistence probability are evaluated. The expression for the sojourn time is derived for a small external force, and is the sum of two terms, whose explicit forms are obtained in the case of an extended wavepacket. The first term is an increasing function of the dissipation parameter gamma , whereas the second one is strictly due to the presence of the driving force.