Electromagnetic waves experience dispersion and these result in a "chirp" in frequency after traversing some distance. This chirp can be heard when waves from a lightning strike in one magnetic hemisphere of the Earth propagate along magnetic Earth's magnetic field lines through charged particles trapped in them and are received in the other magnetic hemisphere, and are used to estimate distances to Fast Radio Bursts (Just how fast is a Fast Radio Burst thought to be?) since dispersion by the interstellar medium is well-characterized.
Question: Are there conditions under which matter waves of bound systems like molecules experience dispersion? If so, how would it manifest itself experimentally?
I don't know if this is a "for example" or a separate question, but it helps reflect my current lack of understanding of the problem. Atoms and molecules have been demonstrated to exhibit diffraction and even Bragg scattering from electromagnetic standing waves1 when there is a dipole moment. Since diffraction is dispersive, do different "frequency components of the molecule's wave" (whatever that means) get spread out in a sort of a spectrum?
1recent news "Bragg Diffraction of Large Organic Molecules"