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Matrix elements of a many‐particle hamiltonian evaluated using hyperspherical coordinates
Author(s) -
Avery John,
Wen ZhenYi
Publication year - 2009
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.560240826
Subject(s) - hamiltonian (control theory) , hamiltonian matrix , coulomb , harmonics , spherical harmonics , matrix (chemical analysis) , basis function , physics , mathematical physics , classical mechanics , mathematics , quantum mechanics , symmetric matrix , chemistry , eigenvalues and eigenvectors , electron , mathematical optimization , chromatography , voltage
Abstract Two formulas derived in previous articles are used to evaluate the matrix elements of a general many‐particle Hamiltonian. The first formula is an expansion of the Coulomb potential of the system in terms of hyperspherical harmonics, while the second is a general formula for the evaluation of angular integrals in many‐dimensional spaces. These two formulas lead to explicit expressions for the Hamiltonian matrix elements when the basis functions are mononomials in the 3 N coordinates multiplied by functions of the hyperradius.