Airy wave packet for a particle in a time-dependent linear potential

2017 ◽  
Vol 70 (2) ◽  
pp. 119-121
Author(s):  
Mounira Berrehail ◽  
Nadjet Benchiheub
Keyword(s):  
Wave Packet ◽  
Time Dependent ◽  
Linear Potential ◽  
Airy Wave Packet

Quantum theory of a non-Hermitian time-dependent forced harmonic oscillator having 𝒫𝒯 symmetry

2019 ◽  
Vol 34 (30) ◽  
pp. 1950187 ◽  
Author(s):  
I. A. Pedrosa ◽  
B. F. Ramos ◽  
K. Bakke ◽  
Alberes Lopes de Lima
Keyword(s):  
Quantum Theory ◽  
Wave Packet ◽  
Harmonic Oscillator ◽  
Driving Force ◽  
Time Dependent ◽  
Complex Numbers ◽  
Linear Potential ◽  
Expectation Values ◽  
Uncertainty Product ◽  
Dependent Mass

We discuss the quantum theory of an harmonic oscillator with time-dependent mass and frequency submitted to action of a complex time-dependent linear potential with [Formula: see text] symmetry. Combining the Lewis and Riesenfeld approach to time-dependent non-Hermitian Hamiltonians having [Formula: see text] symmetry and linear invariants, we solve the time-dependent Schrödinger equation for this problem and use the corresponding quantum states to construct a Gaussian wave packet solution. We show that the shape of this wave packet does not depend on the driving force. Afterwards, using this wave packet state, we calculate the expectation values of the position and momentum, their fluctuations and the associated uncertainty product. We find that these expectation values are complex numbers and as a consequence the position and momentum operators are not physical observables and the uncertainty product is physically unacceptable.

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

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.

Time-dependent wave packet study on trans-cis isomerization of HONO

2004 ◽  
Vol 120 (13) ◽  
pp. 6072-6084 ◽  
Author(s):  
Falk Richter ◽  
Pavel Rosmus ◽  
Fabien Gatti ◽  
Hans-Dieter Meyer
Keyword(s):  
Wave Packet ◽  
Time Dependent

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

QUANTUM DYNAMICS OF WAVE PACKET IN HARMONIC POTENTIAL

2005 ◽  
Vol 19 (24) ◽  
pp. 3745-3754
Author(s):  
ZHAN-NING HU ◽  
CHANG SUB KIM
Keyword(s):  
Schrödinger Equation ◽  
Wave Packet ◽  
Quantum Dynamics ◽  
Schrodinger Equation ◽  
Analytic Solution ◽  
Nonlinear Differential Equations ◽  
Time Dependent ◽  
Dimensional System ◽  
Two Dimensional ◽  
Vibrational States

In this paper, the analytic solution of the time-dependent Schrödinger equation is obtained for the wave packet in two-dimensional oscillator potential. The quantum dynamics of the wave packet is investigated based on this analytic solution. To our knowledge, this is the first time we solve, analytically and exactly this kind of time-dependent Schrödinger equation in a two-dimensional system, in which the Gaussian parameters satisfy the coupled nonlinear differential equations. The coherent states and their rotations of the system are discussed in detail. We find also that this analytic solution includes four kinds of modes of the evolutions for the wave packets: rigid, rotational, vibrational states and a combination of the rotation and vibration without spreading.

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