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A new approach to the quantum mechanics of atoms and small molecules
Author(s) -
Avery John,
Antonsen Frank
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.560360820
Subject(s) - wave function , orthonormality , bound state , physics , generalization , hydrogen atom , quantum mechanics , schrödinger equation , basis set , basis (linear algebra) , binding energy , coulomb , atom (system on chip) , mathematical physics , classical mechanics , molecule , mathematics , mathematical analysis , orthonormal basis , group (periodic table) , geometry , electron , computer science , embedded system
When the Schrödinger equation for a system of N particles interacting through Coulomb forces is expressed in terms of hyperspherical coordinates, it closely resembles the d ‐dimensional generalization of the hydrogen atom wave equation (where d = 3 N ). The d ‐dimensional hydrogenlike wave functions can be found exactly, and a set of these functions, all corresponding to the same energy (but to different charges), fulfills a potential weighted orthonormality relation. When such a set of “generalized Coulomb Sturmians” is used as a basis set for bound states, solution of the resulting secular equations yields a spectrum of parameters k 0 , which are proportional to the square roots of the binding energies. These parameters also govern the asymptotic behavior of the basis set appropriate for the expansion of the bound states to which they correspond.