On the Interpretation of the 'Extra' Variables in the Hurwitz   Transformation
  The Hurwits transformation is generalized by introducing three new variables called 'extra'. Interpretation of these extra variables allows us to establish relation between isotropic harmonic oscillator and five-dimensional hydrogen-like atom in 'electromagnetic' fields of various configurations. For the Schrodinger equations, the scheme of separation of extra variables is suggested. 
Le Van Hoang, Nguyen Thanh Son