Approximate separation of the hyperradius in the many‐particle Schrödinger equation | Zendy

Avery J. | Zendy; Goodson D. Z. | Zendy; Herschbach D. R. | Zendy

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Approximate separation of the hyperradius in the many‐particle Schrödinger equation

Author(s) -

Avery J.,

Goodson D. Z.,

Herschbach D. R.

Publication year - 1991

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.560390503

Subject(s) - physics , scaling , effective nuclear charge , particle (ecology) , radial function , function (biology) , helium atom , charge (physics) , dimension (graph theory) , atom (system on chip) , schrödinger equation , atomic physics , helium , mathematical physics , quantum mechanics , mathematical analysis , mathematics , electron , geometry , combinatorics , oceanography , evolutionary biology , computer science , biology , embedded system , geology

For large values of d = 3 N , the radial distribution function of an N ‐particle system is sharply peaked near the hyperradius r m = ( d − 2)/2 k 0 , where k 0 ≡(2/ E /) 1/2 . This fact allows an approximate separation of the hyperradius, leading to many‐dimensional hydrogenlike radial solutions. Kindred applications to dimensional scaling are also discussed, where d = DN , with D the spatial dimension. For the large D regime, illustrative analytic formulas are obtained giving the energy and effective nuclear charge for the lowest few S states of the helium atom.

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