Integral Equation-Based Numerical Methods for the Time-Dependent Schrödinger Equation

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" Integral Equation-Based Numerical Methods for the Time-Dependent Schrödinger Equation "
Kaye, Jason Greengard, Leslie

Document Type	:	Latin Dissertation
Language of Document	:	English
Record Number	:	1113882
Doc. No	:	TLpq2394293355
Main Entry	:	Greengard, Leslie
	:	Kaye, Jason
Title & Author	:	Integral Equation-Based Numerical Methods for the Time-Dependent Schrödinger Equation\ Kaye, JasonGreengard, Leslie
College	:	New York University
Date	:	2020
student score	:	2020
Degree	:	Ph.D.
Page No	:	137
Abstract	:	In the first part of this dissertation, we introduce a new numerical method for the solution of the time-dependent Schrodinger equation (TDSE) with a smooth potential, based on its reformulation as a Volterra integral equation. We present versions of the method both for periodic boundary conditions, and for free space problems with compactly supported initial data and potential. A spatially uniform electric field may be included, making the solver applicable to simulations of light-matter interaction.
Subject	:	Contour deformation
	:	Integral equations
	:	Light-matter interaction
	:	Pseudospectral methods
	:	Time-dependent Schrödinger equation
	:	Transparent boundary conditions