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Symbolic computation in quantum mechanics. Several simple examples
Author(s) -
Čížek J.,
Vinette F.
Publication year - 1988
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.560340858
Subject(s) - fortran , maple , symbolic computation , computer science , computation , subroutine , notation , programming language , algebra over a field , mathematics , pure mathematics , arithmetic , mathematical analysis , botany , biology
The aim of this article is to illustrate the use of symbolic computation in solving some problems in quantum theory. Emphasis will be given to the possibility of manipulating expressions symbolically and to the interface of numerical and algebraic languages. The illustrate the use of the scientific computation language Maple as a research tool, we present our work on lower energy bounds for anharmonic oscillators and on the spherical Zeeman effect. Another example consists in the perturbation calculations of the N ‐dimensional hydrogen atom, keeping the quantum labels in general form. Further, we describe the interface of Maple, Fortran, and the typesetting language, Troff. The basic feature is illustrated on the application of the inner projection technique and of the method of intermediate Hamiltonians on the benzene molecule as well as on the geminal approach to the butadiene molecule; the main calculations were first done in Maple and then transferred into Fortran's notation so that Fortran subroutines could be used. Finally, the results either in Maple or in Fortran can be transferred to a Troff file.