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A formulation of the quantum‐mechanical many‐body problem in terms of hyperspherical coordinates
Author(s) -
Avery John,
ZhenYi Wen
Publication year - 1984
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.560250612
Subject(s) - hamiltonian (control theory) , yukawa potential , representation (politics) , wave function , basis (linear algebra) , quantum , classical mechanics , physics , matrix (chemical analysis) , matrix representation , hamiltonian matrix , construct (python library) , basis function , mathematical physics , quantum mechanics , mathematics , symmetric matrix , chemistry , computer science , group (periodic table) , geometry , eigenvalues and eigenvectors , mathematical optimization , chromatography , politics , political science , law , programming language
Hyperspherical coordinates are used to construct a matrix representation of a general N ‐particle Hamiltonian in the case where the interaction is electrostatic. The Yukawa interaction can be treated similarly, as is shown in an appendix. The basis functions used to construct the matrix representation of H are mononomials inthe 3 N coordinates of the particles, multiplied by functions of the hyperradius. Methods for transforming from this representation to a symmetry‐adapted representation are also discussed.