THEORY OF THE GENERALIZED KUSTAANHEIMO-STIEFEL TRANSFORMATION

The theory of the generalized KS transformation is given for the Keple r problem in q + 1 dimensions (q = 2h, h = 0, 1, 2,...). We prove the following statement: The Kepler problem in (q + 1)-dimensional real sp ace and the problem of an isotropic harmonic oscillator in a real spac e of dimension N can be connected via a generalized KS transformation only for the cases N = 2q and q = 2h (h = 0, 1, 2,...). We also sugges t a simple graphical method of establishing the appropriate generalize d KS transformation.