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Direct solution of the Schrödinger equation by a parallel genetic algorithm: Cases of an exactly solvable 2‐D interacting oscillator and the hydrogen atom
Author(s) -
Saha Rajendra,
Bhattacharyya S. P.,
Taylor Christopher D.,
Zhao Yong,
Cundari Thomas R.
Publication year - 2003
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.10685
Subject(s) - schrödinger equation , hydrogen atom , wave function , quantum , quadrature (astronomy) , fourier transform , atom (system on chip) , kinetic energy , physics , mathematics , quantum mechanics , computer science , optics , parallel computing , group (periodic table)
The Schrödinger equation for an exactly solvable 2‐D interacting oscillator problem is solved numerically by application of a parallel genetic algorithm on a fixed coordinate grid ( n × n ). The critical energy evaluation step for the wave function strings is parallelized. A fast Fourier transform is used for computing the kinetic energy while the potential energy is obtained by quadrature. Comparison with the exact result indicates viability of the method. As a second case, the hydrogen atom problem is solved by the same method. Parallel performance of the code is also assessed. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 243–250, 2003