The time-dependent Schrodinger equation in three dimensions under geometric constraints

We consider a quantum motion governed by the time-dependent Schrodinger equation on a three dimensional comb structure. We derive the corresponding fractional Schrodinger equations for the reduced probability density functions by projection of the three dimensional comb dynamics in the two- and one-dimensional configuration space. This represents another physical example of a system where fractional calculus emerges. We give closed-form solutions of the corresponding equations for the reduced probability density functions in terms of the Fox H-function, by using the Green's function approach. Published under license by AIP Publishing.