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The time-dependent Schr\"odinger equation is solved formally for an atomic or molecular system which is subjected simultaneously to a rotating magnetic field of constant amplitude and angular velocity and to a constant magnetic field along the axis of rotation. The method yields the transition probabilities in terms of the solutions to an eigenvalue problem. This eigenvalue problem is solved both for (a) a normal Zeeman effect and for (b) the case where a transition from a given level is isolated in frequency from other transitions from the same level. Case (a) is exactly soluble and yields a solution which is shown to be the same as that of Bloch and Rabi, but is in a form which is more convenient for integration over the velocity distribution. Case (b) must be solved by an approximate method which results in a prediction of multiple quantum transitions as observed by Kusch.
Harold Salwen (Mon,) studied this question.