scholarly journals CombinedR-matrix eigenstate basis set and finite-difference propagation method for the time-dependent Schrödinger equation: The one-electron case

2008 ◽  
Vol 78 (6) ◽  
Author(s):  
L. A. A. Nikolopoulos ◽  
J. S. Parker ◽  
K. T. Taylor
Keyword(s):  
Finite Difference ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Basis Set ◽  
The One

A Refined Speed Limit for the Imaginary-Time Schrödinger Equation

2020 ◽  
Vol 27 (02) ◽  
pp. 2050010
Author(s):  
Jie Sun ◽  
Songfeng Lu
Keyword(s):  
Schrödinger Equation ◽  
Quantum Dynamics ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Uncertainty Relations ◽  
Speed Limit ◽  
Full Time ◽  
Imaginary Time ◽  
Full Solution ◽  
The One

Recently, Kieu proposed a new class of time-energy uncertainty relations for time-dependent Hamiltonians, which is not only formal but also useful for actually evaluating the speed limit of quantum dynamics. Inspired by this work, Okuyama and Ohzeki obtained a similar speed limit for the imaginary-time Schrödinger equation. In this paper, we refine the latter one to make it be further like that of Kieu formally. As in the work of Kieu, only the initial states and the Hamiltonians, but neither the instantaneous eigenstates nor the full time-dependent wave like functions, which would demand a full solution for a time-dependent system, are required for our optimized speed limit. It turns out to be more helpful for estimating the speed limit of an actual quantum annealing driven by the imaginary-time Schrödinger equation. For certain case, the refined speed limit given here becomes the only useful tool to do this estimation, because the one given by Okuyama and Ohzeki cannot do the same job.

Remarks on discrete and semi-discrete transparent boundary conditions for solving the time-dependent Schrödinger equation on the half-axis

2016 ◽  
Vol 31 (1) ◽  
Author(s):  
Alexander Zlotnik ◽  
Ilya Zlotnik
Keyword(s):  
Finite Difference ◽  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Finite Difference Schemes ◽  
Transparent Boundary Conditions ◽  
Space Step ◽  
Half Axis ◽  
Generalized Time

AbstractWe consider the generalized time-dependent Schrödinger equation on the half-axis and a broad family of finite-difference schemes with the discrete transparent boundary conditions (TBCs) to solve it. We first rewrite the discrete TBCs in a simplified form explicit in space step

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