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Direct solution of the many‐body schröudinger equation in the hyperspherical formalism: Application of the HH–GLF method to the positronium ion e + e − e +
Author(s) -
Bian Wensheng,
Deng Conghao
Publication year - 1994
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.560500603
Subject(s) - physics , formalism (music) , eigenvalues and eigenvectors , spherical harmonics , harmonics , schrödinger equation , ground state , quantum mechanics , computational physics , art , musical , voltage , visual arts
We apply the HH – GLF method, a new simple hyperspherical harmonic method proposed recently by one of us, to directly solve the three‐body Schrödinger equation for e + e − e + . Uniformally convergent energy eigenvalues are obtained with only several GLF and the obtained ground‐state energy with 200 HH and 6 GLF is −0.26124 au, which is very near the exact value of −0.26200 au. Energy results for maximum global momentum Km ≤ 20 are compared with those from some other hyperspherical techniques carefully, and we find that, in the example of e + e − e + , the HH – GLF method can yield results as accurate as the best available other HH method, but is conceptually simpler and more convenient for practical calculations with a large number of hyperspherical harmonics. © 1994 John Wiley & Sons, Inc.