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A new algebraic approach to the eigenvalue problems of linear differential operators without integrations
Author(s) -
Demiralp Metin
Publication year - 1986
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.560290212
Subject(s) - pointwise , eigenvalues and eigenvectors , algebraic number , mathematics , basis (linear algebra) , hamiltonian (control theory) , set (abstract data type) , scheme (mathematics) , differential (mechanical device) , algebra over a field , mathematical analysis , mathematical optimization , pure mathematics , computer science , quantum mechanics , physics , geometry , thermodynamics , programming language
In this work, a new approximation scheme based on the evaluation of the pointwise expectation of the Hamiltonian ( H ) via a conveniently chosen basis set is proposed. This scheme does not necessitate integration; however, physical and mathematical considerations in choosing the basis set are considerably important when very precise and rapidly convergent results are desired. In this method, the best linear combination of “well‐selected” basis functions are sought in a way such that H ψ / ψ is flat in the neighborhood of a conveniently chosen point in the domain of H . This yields an algebraic eigenvalue problem. Some concrete applications that have already been realized confirm the efficiency of this approach.