CONTINUATION OF THE SCHRODINGER-EQUATION FOR HIGHER ANGULAR-MOMENTUM STATES TO D-DIMENSION AND INTERDIMENSIONAL DEGENERACIES

The application of the techniques of dimensional scaling, and in parti cular the 1/D expansion, to higher angular-momentum states of multiele ctron atoms requires the generalized Euler angles, which multiply with increasing D to be ''factored out'' of the wave function. The factori zation must be performed in a way that produces from the Schrodinger e quation a tractable set of differential equations which admit continua tion in the dimension D. In two recent works the authors have achieved the necessary factorization of the wave function by generalizing the Schwartz expansion to N electrons in D dimensions. The present paper a pplies the N-electron D-dimensional Schwartz expansion to the two-elec tron problem in D dimensions. The resulting set of coupled differentia l equations in the internal variables admit continuation in D, enablin g the methods of dimensional scaling to be applied to higher-angular-m omentum states. In addition, the coupled differential equations clearl y show the complete spectrum of exact interdimensional degeneracies of the two-electron system.