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Physical Review A

Comment on “Time-dependent general quantum quadratic Hamiltonian system”

Yujun Zheng

Published Dec 15, 2006• 4 citations
Publisher

Abstract

It is shown that the propagator and wave function recently found by are not complete and the results are not correct for constant coefficients of a time-dependent general quantum quadratic Hamiltonian for the case of . We presented the correct evolution operator, propagator, and wave function of the general time-dependent quantum quadratic Hamiltonian system.

DOI
10.1103/physreva.74.066101

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Reply to “Comment on ‘Time-dependent general quantum quadratic Hamiltonian system” ’

Kyu Hwang Yeon, Chung‐In Um, Thomas F. George

In reply to the Comment by Zheng [Phys. Rev. A 68, 052108 (2003)], it is reaffirmed that the propagator and wave function derived originally are correct.Received 26 October 2006DOI:https://doi.org/10.1103/PhysRevA.74.066102©2006 American Physical Society

Physical Review A•Dec 15, 2006•0 citations

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Exact quantum solutions of general driven time‐dependent quantum quadratic system

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Abstract We studied the general time‐dependent linear and quadratic system via dynamical symmetries. In an algebraic framework, we obtained exact solutions of the evolution operators, propagators, and wave functions of the general time‐dependent linear and quadratic system. To illustrate our calculations, we discuss a few special cases, including a particle driven by a monochromatic electric field, and cases of oscillatory, linear, or monotonic with respect to the time of the quadratic system. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

International Journal of Quantum Chemistry•Nov 28, 2006•3 citations
It is shown that the propagator and wave function recently found by are not complete and the results are not correct for constant coefficients of a time-dependent general quantum quadratic Hamiltonian for the case of . We presented the correct evolution operator, propagator, and wave function of the general time-dependent quantum quadratic Hamiltonian system.
We use the evolution operator method to describe time-dependent quadratic quantum systems in the framework of nonrelativistic quantum mechanics. For simplicity, we consider a free particle with a variable mass M(t), a particle with a variable mass M(t) in an alternating homogeneous field, and a harmonic oscillator with a variable mass M(t) and frequency ω(t) subject to a variable force F(t). To construct the evolution operators for these systems in an explicit disentangled form, we use a simple technique to find the general solution of a certain class of differential and finite-difference nonstationary Schrödinger-type equations of motion and also the operator identities of the Baker–Campbell–Hausdorff type. With known evolution operators, we can easily find the most general form of the propagators, invariants of any order, and wave functions and establish a unitary relation between systems. Results known in the literature follow from the obtained general results as particular cases.
Abstract We studied the general time‐dependent linear and quadratic system via dynamical symmetries. In an algebraic framework, we obtained exact solutions of the evolution operators, propagators, and wave functions of the general time‐dependent linear and quadratic system. To illustrate our calculations, we discuss a few special cases, including a particle driven by a monochromatic electric field, and cases of oscillatory, linear, or monotonic with respect to the time of the quadratic system. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007