Can matter waves of bound systems experience dispersion? If so, how would it manifest itself experimentally? 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"

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*https://phys.org/news/2020-07-diffract-molecules.html

*https://physics.aps.org/articles/v13/s93

*https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.033604
 A: 
Can matter waves of bound systems experience dispersion? If so, how would it manifest itself experimentally

Electromagnetic waves have variations in energy as a function of (x,y,z,t)
The quantum mechanical waves that describe particles and molecules are not energy waves. Each particle/molecule is described by a wavefunction $Ψ$ , a complex function which is a solution of the quantum mechanical equation, BUT is not measureable. What is measured in experiments is  $Ψ^*Ψ$ which , according to the postulates of quantum mechanics, is a probability to find the particle/molecule at (x,y,z,t). See the double slit experiment one electron at a time

Each electron is a dot seemingly random, the wave nature appears with the accumulation of events which is a probability distribution.
So any type of interference is possible ,but it will manifest itself in the probability distributions , in no sense in matter waves that can be timed, as far as I can see.
As far as "chirps" concerned: we are in the QM regime when talking of bound states. They are quantum mechanically bound, and described mathematically by QM wavefunctions. This means that any single measurement can show no chirps. Any chirps will be seen in the probability distributions.
A: As stated in the comment by @ChiralAnomaly, all wave packets corresponding to particles with nonzero mass should experience dispersion, because velocity is (classically) proportional to momentum and all wave packets have a spread of momentum due to the uncertainty principle.
An experiment to prove this dispersion would be relatively easy:  for example, diffraction of a particle beam by a crystal will produce first- and second- order beams with angular spread that depends on the momentum spread of the original wave packets of the particles.
A single detected particle does not exhibit dispersion, because (if its velocity is detected) it can only have one velocity.  Dispersion and wave phenomena in general are features of the probability distribution, which can only be measured  in the form of a large number of detections of particles associated with identical wave packets.
In the case of a bound particle such as an electron in a hydrogen atom, it's not obvious what "dispersion" would mean.  However if the velocity of the electron could be measured at exactly the same point for a large number of identical atoms, the magnitude of the velocity would always be the same because the energy spectrum is discrete.  The direction of the velocity would vary randomly.  So, if "dispersion" means having a spread of magnitude of velocity, there is no dispersion on a typical bound system.  If there are some bound systems without discrete energy spectra, those systems would exhibit "dispersion" in that sense.
