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The quantum mechanical many‐body problem in hyperspherical coordinates. Analysis of systems with coulomb interactions in terms of many‐dimensional hydrogen‐like wave functions
Author(s) -
Avery John,
Larsen Peter Sommer,
Hengyi Shen
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.560290112
Subject(s) - eigenfunction , wave function , angular momentum , solid harmonics , physics , harmonics , clebsch–gordan coefficients , coulomb , spin weighted spherical harmonics , total angular momentum quantum number , schrödinger equation , quantum mechanics , momentum (technical analysis) , quantum , classical mechanics , spherical harmonics , quantum number , eigenvalues and eigenvectors , electron , finance , voltage , economics , irreducible representation
A method is described for using many‐dimensional hydrogen‐like wave functions as a starting point for constructing solutions to the Schrödinger equation of an N ‐particle system. The solutions are built up from symmetry‐adapted hyperspherical harmonics, multiplied by functions of the hyperradius, r . Approximate asymptotic solutions for large values of r are discussed, as well as approximate solutions valid near r = 0. Properties of hyperspherical harmonics are discussed. General methods are presented for resolving arbitrary functions into hyperspherical harmonics and for constructing simultaneous eigenfunctions of generalized angular momentum and total orbital angular momentum.