The Mössbauer effect explained

Direct integration of Schrödinger's equation yields the transition probability for the Mössbauer effect, assuming that the bound nucleus receives a sudden impulse of momentum from a gamma particle. Generalization from two coupled oscillators to a linear chain introduces the discrete Fourier transform, in real variables. This chain of coupled oscillators can be used to suggest how very low order collective modes can remain unexcited by the impact.