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Method of computer algebraic calculation of the matrix elements in the second quantization language
Author(s) -
Gotoh Masashi,
Mori Kazuhide,
Itoh Reikichi
Publication year - 1995
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.560560304
Subject(s) - algebraic expression , creation and annihilation operators , annihilation , matrix (chemical analysis) , unitary state , quantization (signal processing) , computer science , algebra over a field , second quantization , algebraic number , matrix element , field (mathematics) , quantum , mathematics , physics , algorithm , chemistry , pure mathematics , quantum mechanics , particle physics , mathematical analysis , chromatography , political science , law
An automated method by the algebraic programming language REDUCE3 for specifying the matrix elements expressed in second quantization language is presented and then applied to the case of the matrix elements in the TDHF theory. This program works in a very straightforward way by commuting the electron creation and annihilation operators ( a † and a ) until these operators have completely vanished from the expression of the matrix element under the appropriate elimination conditions. An improved method using singlet generators of unitary transformations in the place of the electron creation and annihilation operators is also presented. This improvement reduces the time and memory required for the calculation. These methods will make programming in the field of quantum chemistry much easier. © 1995 John Wiley & Sons, Inc.