Motion of a particle in a gravitational field and reflecting floor: The potential takes the form
V(z)={gz∞z>0z<0.
(a) Solve the corresponding Schr\"odinger equation exactly using the Airy functions. (Remark: the same problem occurs in the motion of electrons in a semiconducting half-space under the action of an electric field.)
(b) Carry out a variational ansatz as in Problem 11.7 for the ground state.