The agreement between quantum-mechanical predictions and experiments has so firmly established the validity of quantum mechanics that we might question the need for further tests. For example, the observed energy levels of hydrogen are in excellent agreement with quantum-mechanical predictions. However, to a large extent this agreement can be regarded more as a test of the specific Hamiltonian used, than of quantum mechanics itself. It should be possible to test the basic framework of quantum mechanics independently of and to much greater accuracy than that provided by such specific predictions. Recently, Weinberg1 has formulated a general framework which introduces nonlinear corrections to quantum mechanics and enables such a test. He suggested that a sensitive test could be made for the presence of such a nonlinearity by slowly driving a resonant transition which transfers a quantum system from one state to another. The effect of the nonlinearity is to make the effective resonance frequency a function of the state probabilities. Thus, the resonance frequency changes as the quantum system is driven from one state to the other, and the applied perturbation (assumed to be monochromatic) cannot stay in resonance through the entire transition. The system will never be driven completely to the other state. This effect would not be observed, that is, the transition could still be driven, if the maximum frequency shift were much less than 1/T. Here, T is the time required to drive the transition if there is no nonlinearity.