Gaussian Wave Packet for Time-dependent Hamiltonian Systems Involving Quadratic, Inverse Quadratic, and (1/x)p + p(1/x) Terms

2011 ◽  
Vol 58 (1) ◽  
pp. 154-157 ◽  
Author(s):  
S. Menouar ◽  
M. Maamache ◽  
H. Bekkar ◽  
Jeong Ryeol Choi
Keyword(s):  
Wave Packet ◽  
Hamiltonian Systems ◽  
Time Dependent ◽  
Gaussian Wave Packet

GEOMETRIC PHASES, SQUEEZED QUANTUM STATES AND GAUSSIAN WAVE PACKET STATES OF RELIC GRAVITONS

2012 ◽  
Vol 18 ◽  
pp. 13-17
Author(s):  
K. BAKKE ◽  
I. A. PEDROSA ◽  
C. FURTADO
Keyword(s):  
Wave Packet ◽  
Linear Time ◽  
Invariant Operator ◽  
Quantum States ◽  
Time Dependent ◽  
Gaussian Wave Packet ◽  
Geometric Phases ◽  
Uncertainty Product ◽  
Quantized Field ◽  
Generalized Time

In this contribution, we discuss quantum effects on relic gravitons described by the Friedmann-Robertson-Walker (FRW) spacetime background by reducing the problem to that of a generalized time-dependent harmonic oscillator, and find the corresponding Schrödinger states with the help of the dynamical invariant method. Then, by considering a quadratic time-dependent invariant operator, we show that we can obtain the geometric phases and squeezed quantum states for this system. Furthermore, we also show that we can construct Gaussian wave packet states by considering a linear time-dependent invariant operator. In both cases, we also discuss the uncertainty product for each mode of the quantized field.

Solving Time-dependent Schrödinger Equation Using Gaussian Wave Packet Dynamics

2018 ◽  
Vol 73 (9) ◽  
pp. 1269-1278
Author(s):  
Min-Ho Lee ◽  
Chang Woo Byun ◽  
Nark Nyul Choi ◽  
Dae-Soung Kim
Keyword(s):  
Schrödinger Equation ◽  
Wave Packet ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Gaussian Wave Packet ◽  
Wave Packet Dynamics

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

2015 ◽  
Vol 93 (8) ◽  
pp. 841-845 ◽  
Author(s):  
I.A. Pedrosa ◽  
Alberes Lopes de Lima ◽  
Alexandre M. de M. Carvalho
Keyword(s):  
Wave Packet ◽  
Harmonic Oscillator ◽  
Uncertainty Relation ◽  
Quantum Correlations ◽  
Wave Functions ◽  
Time Dependent ◽  
Gaussian Wave Packet ◽  
Order Ordinary Differential Equation ◽  
Quantum Invariant ◽  
Dependent Mass

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.

Time-dependent wave-packet approach to the quantum transport of carbon nanotubes with vacancies

2007 ◽  
Vol 601 (22) ◽  
pp. 5266-5269 ◽  
Author(s):  
Hiroyuki Ishii ◽  
Nobuhiko Kobayashi ◽  
Kenji Hirose
Keyword(s):  
Carbon Nanotubes ◽  
Wave Packet ◽  
Quantum Transport ◽  
Time Dependent

A comparative study of time dependent quantum mechanical wave packet evolution methods

1992 ◽  
Vol 96 (3) ◽  
pp. 2077-2084 ◽  
Author(s):  
Thanh N. Truong ◽  
John J. Tanner ◽  
Piotr Bala ◽  
J. Andrew McCammon ◽  
Donald J. Kouri ◽  
...  
Keyword(s):  
Wave Packet ◽  
Comparative Study ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Mechanical Wave ◽  
Quantum Mechanical Wave Packet
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