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 +

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.