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Iterative determination of eigenvalues of the time‐independent Schrödinger equation by the use of the generalized Bloch equation
Author(s) -
Meißner Holger,
Steinborn E. Otto
Publication year - 1997
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/(sici)1097-461x(1997)63:1<257::aid-qua27>3.0.co;2-7
Subject(s) - eigenfunction , eigenvalues and eigenvectors , wave function , schrödinger equation , hamiltonian (control theory) , mathematical physics , anharmonicity , quartic function , quantum mechanics , ground state , physics , hamiltonian matrix , orthonormal basis , mathematics , mathematical analysis , symmetric matrix , mathematical optimization , pure mathematics
Recently, we proposed an iteration method for solving the eigenvalue problem of the time‐independent Schrödinger equation [H. Meißner and E. O. Steinborn, Int. J. Quantum Chem. 61, 777 (1997)]. The eigenfunctions are expanded in terms of a basis set. The wave‐function expansion coefficients (WECs) are matrix elements of the wave operator. They are determined iteratively by utilizing a reference space, the concept of an effective Hamiltonian, and the generalized Bloch equation. In this article, the WEC iteration method is applied to the calculation of the ground state and of some excited states of a quartic anharmonic oscillator, i.e., a Boson system, using a large reference space, as well as of the H 2 O molecule, i.e., a Fermion system. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 257–268 1997