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Application of finite‐element method to the two‐dimensional Schrödinger equation
Author(s) -
Sato Nobuyuki,
Iwata Suehiro
Publication year - 1988
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540090306
Subject(s) - supercomputer , cartesian coordinate system , coordinate system , hamiltonian (control theory) , finite element method , schrödinger equation , scheme (mathematics) , physics , mathematics , mathematical analysis , computer science , geometry , mathematical optimization , thermodynamics , operating system
Abstract An algorithm to solve the two‐dimensional Schrödinger equation based on the finite‐element method is proposed. In our scheme, the molecular Hamiltonian with any arbitrary internal coordinate system can be solved as easily as with the Cartesian coordinate system. The efficient computer program based on the algorithm was developed on the HITAC S‐810 supercomputer. The performance of the program is examined in the following test problems; (1) free particle in a box, (2) linear triatomic molecule with two equal force constants, (3) coupled Morse oscillators, (4) Henon‐Heiles potential, (5) H 3 O + symmetric vibrational modes. The algorithm is demonstrated to be very suited for the vector‐type supercomputer.