scholarly journals Quantization of time-dependent singular potential systems in one-dimension by using the Nikiforov-Uvarov method

2015 ◽  
Vol 67 (7) ◽  
pp. 1127-1132 ◽  
Author(s):  
Salah Menouar ◽  
Jeong Ryeol Choi
Keyword(s):  
Singular Potential ◽  
Time Dependent ◽  
One Dimension ◽  
Uvarov Method

scholarly journals Dynamics of entanglement entropy of interacting fermions in a 1D driven harmonic trap

2018 ◽  
Vol 175 ◽  
pp. 03002
Author(s):  
Joshua R. McKenney ◽  
William J. Porter ◽  
Joaquín E. Drut
Keyword(s):  
Thermal Behavior ◽  
Parametric Resonance ◽  
Cold Atoms ◽  
Particle System ◽  
Entanglement Entropy ◽  
Harmonic Trap ◽  
Time Dependent ◽  
One Dimension ◽  
Recent Analysis ◽  
Contact Interactions

Following up on a recent analysis of two cold atoms in a time-dependent harmonic trap in one dimension, we explore the entanglement entropy of two and three fermions in the same situation when driven through a parametric resonance. We find that the presence of such a resonance in the two-particle system leaves a clear imprint on the entanglement entropy. We show how the signal is modified by attractive and repulsive contact interactions, and how it remains present for the three-particle system. Additionaly, we extend the work of recent experiments to demonstrate how restricting observation to a limited subsystem gives rise to locally thermal behavior.

Time-Dependent States in One Dimension

2008 ◽  
pp. 1-29
Author(s):  
Charles E. Burkhardt ◽  
Jacob J. Leventhal
Keyword(s):  
Time Dependent ◽  
One Dimension

scholarly journals Quantization of a 3D Nonstationary Harmonic plus an Inverse Harmonic Potential System

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Salim Medjber ◽  
Hacene Bekkar ◽  
Salah Menouar ◽  
Jeong Ryeol Choi
Keyword(s):  
Separation Of Variables ◽  
Type Equation ◽  
Invariant Operator ◽  
Wave Functions ◽  
Time Dependent ◽  
Harmonic Potential ◽  
Uncertainty Relations ◽  
Mathematical Methods ◽  
Potential System ◽  
Uvarov Method

The Schrödinger solutions for a three-dimensional central potential system whose Hamiltonian is composed of a time-dependent harmonic plus an inverse harmonic potential are investigated. Because of the time-dependence of parameters, we cannot solve the Schrödinger solutions relying only on the conventional method of separation of variables. To overcome this difficulty, special mathematical methods, which are the invariant operator method, the unitary transformation method, and the Nikiforov-Uvarov method, are used when we derive solutions of the Schrödinger equation for the system. In particular, the Nikiforov-Uvarov method with an appropriate coordinate transformation enabled us to reduce the eigenvalue equation of the invariant operator, which is a second-order differential equation, to a hypergeometric-type equation that is convenient to treat. Through this procedure, we derived exact Schrödinger solutions (wave functions) of the system. It is confirmed that the wave functions are represented in terms of time-dependent radial functions, spherical harmonics, and general time-varying global phases. Such wave functions are useful for studying various quantum properties of the system. As an example, the uncertainty relations for position and momentum are derived by taking advantage of the wave functions.

scholarly journals Time-dependent approach to many-particle tunneling in one dimension

2012 ◽  
Vol 86 (4) ◽  
Author(s):  
Takahito Maruyama ◽  
Tomohiro Oishi ◽  
Kouichi Hagino ◽  
Hiroyuki Sagawa
Keyword(s):  
Time Dependent ◽  
One Dimension
Sign in / Sign up

Export Citation Format

Share Document