Black Body Radiation

At the beginning of the 20th century Quantum Mechanics theory was established. It starts with the discovery of electromagnetic [EM] energy quantization by Max Plank (1900) [1] needed to explain black body radiation distribution as a function of frequency and temperature. He explained it by a model where resonators (latter identified as harmonic oscillators) can emit radiation only by quanta of energy. Later Bohr [2] found the Quantum Mechanical model for the Hydrogen atom, using Planck’s constant as a measure for angular momentum quantization. An important concept in his work was the correspondence principle. According to this principle the quantum mechanical results should coincide with classical calculation at large quantum numbers.

Einstein used the developing quantum mechanical theory to explain Planck distribution function by investigating the processes of emission and absorption of light by an elementary system [3]. He introduced two coefficients: for the rate of photons spontaneous emission and for photons absorption and stimulated emission rate, per unit electromagnetic density. Einstein didn’t calculate those coefficients. It took another decade till Dirac show how to calculate the coefficients [4] according to quantum mechanical (QM) theory.

Going back to classical theory, only one of the coefficients mentioned above calculated according QM theory is agree with that classical theory calculation. This is the spontaneous emission coefficient. The absorption coefficient calculated classically, usually as a second order effect, is not compatible with the QM result.

It is the aim of this work to show that Plank’s formula for black body spectral density can be calculated from classical theory when Einstein approach to pro...

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...calculations will be confined to a unit volume which is a small part of the overall volume, so that there is no need to worry about boundary condition. The system is in high enough temperature that ensures:

a. There are enough oscillators vibrating with appreciable amplitudes.

b. There is a dense EM field composed of many waves that interfere with each other.

This condition is appropriate for classical calculation of thermal equilibrium through absorption and emission of EM energy.

The interference of waves causes a variable electric field, at each oscillator site, both in direction and in phase, so that the oscillator interacts with an effective wave of constant direction and phase for only short (coherence) time relative to relaxation times and yet longer than the period of the EM wave:

(1)

where is the damping coefficient of oscillators of frequency .