Consider the corresponding problem for a particle confined to the right-hand half of a harmonic-oscillator potential:
V(x) = infinity, x< 0
V(x) = (1/2)Cx^2, x >= 0
a. Compute the allowed wave function for stationary states of this system with those for a normal harmonic oscillator having the same values of m and C.
b. What are the allowed quantized energies of the half-oscillator?
c. Devise a classical mechanical system that would be a macroscopic analog of this quantum-mechanical system.