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Simple Iterative Procedures for Quantum‐Mechanical Bound States
Author(s) -
Burrows Brian L.,
Cohen Maurice,
Feldman Tova
Publication year - 1991
Publication title -
israel journal of chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.908
H-Index - 54
eISSN - 1869-5868
pISSN - 0021-2148
DOI - 10.1002/ijch.199100042
Subject(s) - anharmonicity , chemistry , simple (philosophy) , quantum , bound state , sequence (biology) , convergence (economics) , atom (system on chip) , upper and lower bounds , quantum mechanics , mathematics , statistical physics , mathematical analysis , physics , philosophy , biochemistry , epistemology , computer science , economics , embedded system , economic growth
Iterative methods are developed to obtain approximate solutions for bound states of quantum‐mechanical systems. A sequence of 2 × 2 secular equations is solved, to yield a specified eigensolution to the N × N secular equation. Our simplest procedure ensures convergence only for certain states, but a generalisation appears to converge for any state. Some sample calculations are presented, both for model (anharmonic oscillator) systems and for a two‐electron atom.