Oscillator approach to the problem of the hydrogen atom in a magnetic field and Feneuille scaling

An attempt has been made to derive an expression for the energy for the hydrogen atom in a uniform magnetic field having dependence on only one variable. The Schrodinger equation is transformed by a complex Kustaanheimo-Stiefel transformation to that for a four-dimensional oscillator with a constraint. The equivalent oscillator problem is solved approximately to obtain an expression for the quantity n2E (n being the principal quantum number, E the energy) as a function of a single variable. Agreement with experimental observations is discussed. (author)