Quote by dauto
I think you need to relearn quantum mechanics. Your understanding of quantization is lacking. The boundary conditions gives a discrete set of oscillation modes true, but that's not what quantization is. Quantization is the fact that each mode will be occupied by an integer number of particles. In classical physics each mode may have any amount of energy.

This is probably just a misunderstanding. Apparently, parkner meant boundary conditions for the ##\psi## function of harmonic oscillator. These indeed play role in obtaining preferred values of energy ##(n+\frac{1}{2})h\nu##.