Work fluctuation and its optimal extraction with time dependent harmonic potential from a non-Markovian bath

2019 ◽  
Vol 516 ◽  
pp. 161-171 ◽  
Author(s):  
Bo Xiao ◽  
Renfu Li
Keyword(s):  
Time Dependent ◽  
Harmonic Potential

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.

The Harmonic Potential Theorem for a Quantum System with Time-Dependent Effective Mass

2015 ◽  
Vol 32 (11) ◽  
pp. 110301 ◽  
Author(s):  
Meng-Yun Lai ◽  
Duan-Liang Xiao ◽  
Xiao-Yin Pan
Keyword(s):  
Quantum System ◽  
Effective Mass ◽  
Time Dependent ◽  
Harmonic Potential
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