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An analytic iterative approach to solving the time‐independent Schrödinger equation
Author(s) -
Junkermeier Chad,
Transtrum Mark,
Berrondo Manuel
Publication year - 2008
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.21917
Subject(s) - simple (philosophy) , operator (biology) , computation , schrödinger equation , range (aeronautics) , mathematics , order (exchange) , iterative method , computer science , mathematical analysis , algorithm , philosophy , biochemistry , chemistry , materials science , epistemology , repressor , finance , transcription factor , economics , composite material , gene
In this article, we introduce a simple analytic method for obtaining approximate solutions of the Schrödinger equation for a wide range of potentials in one‐ and two‐dimensions. We define an operator, called the iteration operator, which will be used to solve for the lowest order state(s) of a system. The method is simple in that it does not require the computation of any integrals in order to obtain a solution. We use this method on several potentials which are well understood or even exactly solvable in order to demonstrate the strengths and weaknesses of this method. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009
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