Statistical consequences of the zero-point energy of the harmonic oscillator

In a recent thermodynamic analysis of the harmonic oscillator Boyer has shown, using an interpolation procedure, that the existence of a zero-point energy leads to Planck’s law. We avoid the interpolation procedure by adding a statistical argument to arrive at Planck’s law as a consequence of the existence of the zero-point energy. As in Boyer’s argument, no explicit assumption of quantum mechanics is introduced. We discuss the relation of our results to the analysis of Planck and Einstein which led to the notion of the quantized radiation field. We then inquire into the discrete or continuous behavior of the energy and pinpoint the origin and meaning of the discontinuities. To include zero-point fluctuations (which are neglected in the thermodynamic analysis), we discuss the statistical (in contrast to the purely thermodynamic) description of the oscillator, which accounts for both the thermal and temperature-independent contributions to the dispersion of the energy.