Direct solution of the Schrodinger equation for some muonic molecules

We use the hyperspherical harmonic method developed by us to directly solve the Schrodinger equation for some muonic molecules without recourse to the Born-Oppenheimer approximation. In our method, a kind of simplified potent ial harmonic representation derived by us is used, and analytic expressions for all matrix elements are obtained; the generalized Laguerre function ex pansion method is used in the solution of the coupled differential equation s. The practical calculations yield very good results for the energy. For e xample, we obtain a ground-state energy of - 0.055623 pau for pp mu, - 0.02 9884 dau for dd mu, and -0.020521 tau for tt mu, in good agreement with the exact values of -0.055676 pau, -0.029921 dau, and - 0.020553 tau. The calc ulated energy values for the first excited states of pp mu, dd mu, tt mu ar e also reported. It is shown that, the potential harmonic representation we used is simple and convenient, and the convergence of the basis functions is uniform and rather rapid. (C) 1999 Elsevier Science B.V. All rights rese rved.