周四讨论班：Statistical consequences of the zero-point energy of the harmonic oscillator（邱荣涛）

时间：2010年1月7号 下午 4：30—6：10
地点：18教学楼405室
主讲：邱荣涛

Luis de la Peña, Andrea Valdés-Hernández, and Ana María Cettob, Am. J. Phys. 76 (10), 947, October 2008.

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.