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Symplectic algorithm for use in computing the time‐independent Schrödinger equation
Author(s) -
Liu XueShen,
Su LiWei,
Ding PeiZhu
Publication year - 2001
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.10049
Subject(s) - symplectic geometry , eigenvalues and eigenvectors , schrödinger equation , morse potential , computation , harmonic oscillator , wave function , mathematics , mathematical analysis , mathematical physics , quantum mechanics , physics , algorithm
We present an improved symplectic scheme‐shooting method (ISSSM) for solving the one‐dimensional time‐independent Schrödinger equation. This method is applied to computations of the eigenvalues and wave functions of the hydrogen molecule (H 2 ) and a Morse potential; the method is also applied to computations of the parameters and wave functions of a soft potential. The numerical results are in good agreement with the exact ones or other numerical ones and illustrate that the ISSSM is more effective than the SSSM. Then the ISSSM is extended to solutions of the two‐dimensional time‐independent Schrödinger equation. The eigenvalues of the two‐dimensional harmonic oscillator and the two‐dimensional Henon–Heiles potential are calculated by using the ISSSM. The numerical results illustrate that our method is stable and convergent for two dimensions. © 2001 Wiley Periodicals, Inc. Int J Quantum Chem, 2001