# Blackbody cavity relationship between energy of oscillators and EM radiation

This question is based on Planck's view of blackbody radiation in a cavity. Here is a quote from here:

...where $\langle E \rangle$ is the average energy of the oscillators present on the walls of the cavity (or the electromagnetic radiation in that frequency interval).

My question is why are these the same? and was Planck ignoring any other sources of radiation e.g. an external source?

Furthermore what was plank's postulate? I can think of 2 possibilities:

1. The energy of the oscillator was quantised i.e. had to take energy $nh\nu$ and the energy of the that can be emitted and absorbed by the oscillator was quantised.
2. Or the energy of the oscillator was not quantised and could take any arbitrary value but the energy that could be emitted and absorbed was quantised.

In either case I believe he thought that the energy of the EM could take any value.

• The EM radiation is the excitation by these oscillators. The EM field may be divided to lots of harmonic oscillators and each of them may oscillate. The amplitude measures the strength of the EM wave at a given frequency and direction. In quantum physics, the oscillators have quantized spectrum. The energy above the minimum is an integer multiple of $E=hf$, the energy of the photon, and the integer may be interpreted as the number of photons in the state (photons with the given frequency and direction). – Luboš Motl May 1 '15 at 9:51
• Yes, Planck did not anticipate the quantization of the electrical field itself in this paper. He assumed the quantization to be caused by the quantization of the energy packets exchanged with the oscillators in the wall. – Sebastian Riese May 9 '15 at 19:49

Usually the "oscillators" in a black-body cavity are standing waves (modes) within the cavity. These standing waves are effectively quantum simple harmonic oscillators because of their energy levels. Mode $i$ with frequency $f_i$ can have $n$ photons in it, resulting in the energy of the $m$th mode being $E_i = h f_i \left(n+\frac{1}{2}\right)$. (The $\frac{1}{2}$ doesn't much matter because that energy can't be radiated away.) That is exactly the energy spectrum of a simple harmonic oscillator, so it makes sense to refer to these standing waves as oscillators.
Unlike what the book says, there are discrete modes in a cavity even in classical mechanics. For a 1D cavity of length $L$, the states have discrete wavelengths $\lambda_i = \frac{L}{n_i}$. (Think about the discrete modes of standing waves on a string -- an example often used in introductory physics courses.) However, in deriving the blackbody spectrum, usually the size of the cavity is taken to be large, in which case the energy of the modes become closely spaced so that it makes sense to think of a continuum of states.