Assuming that Vo is very high compared to the quantized energies of low-lying states, obtain an approximate expression for the energy splitting between the two lowest-lying states.

(a) Let y(x,t) be the wave function of a spinless particle corresponding to a plane wave in three dimensions. Show that y*(x, t) is the wave function for the plane wave with the momentum direction reversed.
(b) Let x(în) be the two-component eigenspinor of o. În with eigenvalue +1. Using the explicit form of x(n) (in terms of the polar and azimuthal angles B and y that characterize în), verify that -i 02x*(n) is the two-component eigenspinor with the spin direction reversed.