when we derive a formula for blackbody radiation, we say that each electromagnetic mode has energy nhf, n is an integer, h is Planck's constant f is the frequency of the radiation. We interpret n as the number of photons per mode. However, a deeper QM analysis involves replacing the electromagnetic mode by a harmonic oscillator having energy (n+1/2)hf. What does this 1/2 mean? 1/2 a photon? We also use a normalized Boltzmann probability distribution to complete the calculation, but when we calculate the number of carriers in semiconductor electronics, we use a Fermi Dirac probablity distribution that is in no way normalized. Anybody have a sound explanation?