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Numerical method based on Magnus expansion and a new shooting method for eigenvalues of Schrödinger equation
Author(s) -
Liu XueShen,
Ding PeiZhu
Publication year - 2005
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.20496
Subject(s) - anharmonicity , eigenvalues and eigenvectors , morse potential , shooting method , schrödinger equation , hamiltonian (control theory) , harmonic oscillator , numerical analysis , mathematics , legendre transformation , taylor series , transformation (genetics) , mathematical physics , mathematical analysis , physics , quantum mechanics , chemistry , mathematical optimization , biochemistry , gene , boundary value problem
The one‐dimensional time‐independent Schrödinger equation is transformed into the Hamiltonian canonical equation by means of the Legendre transformation, the numerical method based on the Magnus expansion and the Taylor expansion of the matrix exponential are applied to the numerical solutions, and a new shooting method for eigenvalues is presented. The method is applied to the calculations of the one‐dimensional harmonic oscillator, a doubly anharmonic oscillator, and a Morse potential. The numerical results are in good agreement with the exact results. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005