The debye theory, as given in this chapter, was worked out before it was known that a harmonic oscillator has a "zero-point energy" of hv/2. thus eq. (20) does not give the correct total energy of a solid in the limit t-0, because the average energy per oscillator goes to hv/2, rather than zero, at t 0. starting with this fact, use the debye model to show that the zero-point energy of a solid should be er.