A particle of mass m is in a linear potential V(z)=F∣z∣ for all z (a ``V-shaped'' potential, with no hard wall).
(a) Show that the even-parity solutions are determined by Ai′(u0)=0 and the odd-parity solutions by Ai(u0)=0, where u0 is defined in terms of the energy.
(b) Find the lowest few energy levels for both parities.
(c) How do these compare with the energy levels for the half-space problem (particle bouncing off a floor)?