The magnetic dipole in undulatory mechanics

In the following lines we present a method for the computation of the characteristic values of the parameter contained in linear differential equations. This method is applicable in certain cases when the equation cannot be reduced to the hypergeometric type. As the special example with which to illustrate our procedure we select the motion of an electron in the combined fields of a nucleus and of a magnetic dipole attached to this nucleus. This problem has an interesting bearing on the theory of the spinning electron, as will be fully discussed in section 6.