Unitary Transformation of the Time-dependent Hamilton System for the Linear, the V-shape and the Triangular Well Potentials into the Quadratic Hamiltonian System

2004 ◽  
Vol 4 (4) ◽  
pp. 636-643 ◽  
Author(s):  
Jeong Ryeol Choi .
Keyword(s):  
Hamiltonian System ◽  
Unitary Transformation ◽  
Time Dependent ◽  
Hamilton System ◽  
Quadratic Hamiltonian

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

SU(1,1) LIE ALGEBRA APPLIED TO THE TIME-DEPENDENT QUADRATIC HAMILTONIAN SYSTEM PERTURBED BY A SINGULARITY

2004 ◽  
Vol 18 (26) ◽  
pp. 3429-3441 ◽  
Author(s):  
JEONG RYEOL CHOI ◽  
SEONG SOO CHOI
Keyword(s):  
Hamiltonian System ◽  
Probability Density ◽  
Lie Algebra ◽  
Time Evolution ◽  
Coherent States ◽  
Classical Trajectory ◽  
Quantum States ◽  
Time Dependent ◽  
Expectation Values ◽  
Quadratic Hamiltonian

We realized SU (1,1) Lie algebra in terms of the appropriate SU (1,1) generators for the time-dependent quadratic Hamiltonian system perturbed by a singularity. Exact quantum states of the system are investigated using SU (1,1) Lie algebra. Various expectation values in two kinds of the generalized SU (1,1) coherent states, that is, BG coherent states and Perelomov coherent states are derived. We applied our study to the CKOPS (Caldirola–Kanai oscillator perturbed by a singularity). Due to the damping constant γ, the probability density of the SU (1,1) coherent states for the CKOPS converged to the center with time. The time evolution of the probability density in SU (1,1) coherent states for the CKOPS are very similar to the classical trajectory.

Propagator of a time-dependent unbound quadratic Hamiltonian system

1996 ◽  
Vol 111 (8) ◽  
pp. 963-971 ◽  
Author(s):  
K. H. Yeon ◽  
H. J. Kim ◽  
C. I. Um ◽  
T. F. George ◽  
L. N. Pandey
Keyword(s):  
Hamiltonian System ◽  
Time Dependent ◽  
Quadratic Hamiltonian

Time-dependent general quantum quadratic Hamiltonian system

2003 ◽  
Vol 68 (5) ◽  
Author(s):  
Kyu Hwang Yeon ◽  
Chung In Um ◽  
Thomas F. George
Keyword(s):  
Hamiltonian System ◽  
Time Dependent ◽  
General Quantum ◽  
Quadratic Hamiltonian
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