Eigenstates of a time-dependent quadratic Hamiltonian, a kind of generalized squeezed number states

1992 ◽  
Vol 107 (5) ◽  
pp. 595-602 ◽  
Author(s):  
W. S. Liu ◽  
P. Tombesi
Keyword(s):  
Time Dependent ◽  
Quadratic Hamiltonian

On the Quantization Problem of a Driven Harmonic Oscillator with Time Dependent Mass and Frequency

2003 ◽  
Vol 17 (18) ◽  
pp. 983-990 ◽  
Author(s):  
Swapan Mandal
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Present Solution ◽  
Quadratic Hamiltonian ◽  
Dependent Mass ◽  
Quantization Problem

The quantization of a driven harmonic oscillator with time dependent mass and frequency (DHTDMF) is considered. We observe that the driven term has no influence on the quantization of the oscillator. It is found that the DHTDMF corresponds the general quadratic Hamiltonian. The present solution is critically compared with existing solutions of DHTDMF.

Canonical Perturbation of a Fast Time-Periodic Hamiltonian via Liapunov-Floquet Transformation

1997 ◽  
Author(s):  
Eric A. Butcher ◽  
S. C. Sinha
Keyword(s):  
Perturbation Theory ◽  
Classical Method ◽  
Time Dependent ◽  
Fast Time ◽  
Quadratic Part ◽  
Canonical Perturbation ◽  
Internal Excitation ◽  
Quadratic Hamiltonian ◽  
Unperturbed Part ◽  
Time Periodic

Abstract In this study a possible application of time-dependent canonical perturbation theory to a fast nonlinear time-periodic Hamiltonian with strong internal excitation is considered. It is shown that if the time-periodic unperturbed part is quadratic, the Hamiltonian may be canonically transformed to an equivalent form in which the new unperturbed part is time-invariant so that the time-dependent canonical perturbation theory may be successfully applied. For this purpose, the Liapunov-Floquet (L-F) transformation and its inverse associated with the unperturbed time-periodic quadratic Hamiltonian are computed using a recently developed technique. Action-angle variables and time-dependent canonical perturbation theory are then utilized to find the solution in the original coordinates. The results are compared for accuracy with solutions obtained by both numerical integration and by the classical method of directly applying the time-dependent perturbation theory in which the time-periodic quadratic part is treated as another perturbation term. A strongly excited Mathieu-Hill quadratic Hamiltonian with a cubic perturbation and a nonlinear time-periodic Hamiltonian without a constant quadratic part serve as illustrative examples. It is shown that, unlike the classical method in which the internal excitation must be weak, the proposed formulation provides accurate solutions for an arbitrarily large internal excitation.

Exact quantum theory of a time-dependent bound quadratic Hamiltonian system

1993 ◽  
Vol 48 (4) ◽  
pp. 2716-2720 ◽  
Author(s):  
Kyu Hwang Yeon ◽  
Kang Ku Lee ◽  
Chung In Um ◽  
Thomas F. George ◽  
Lakshmi N. Pandey
Keyword(s):  
Quantum Theory ◽  
Hamiltonian System ◽  
Time Dependent ◽  
Exact Quantum ◽  
Quadratic Hamiltonian

Time-dependent invariant for the quadratic Hamiltonian and the stable squeezed states

1987 ◽  
Vol 65 (5) ◽  
pp. 525-526 ◽  
Author(s):  
Fan Hong-Yi ◽  
H. R. Zaidi
Keyword(s):  
General Expression ◽  
Time Dependent ◽  
Squeezed States ◽  
Quadratic Hamiltonian

The conditions for the existence of a time-dependent invariant for the general quadratic Hamiltonian are investigated. A general expression for such an invariant is obtained, and it is shown that the stable squeezed states are eigenstates of this invariant.

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