Quantum Optics for Engineers

2

Planck’s Quantum Energy Equation

2.1    Introduction

In his work on light sources and black body radiation, Max Planck, around 1900, was confronted with experimental data that could not be explained with the prevailing theoretical concepts of the time. The problem was to express the energy distribution of light emission as a function of wavelength. Using Planck’s own notation (Planck, 1901), the number of electromagnetic modes per unit volume can be expressed as

$u=\frac{8\text{π}{v}^2}{c^3}U$

(2.1)

where

ν is the frequency of the emission, in Hz or cycles per second

c is the speed of light (c = 2.99792458 × 10⁸ ms⁻¹)

Then the question becomes how to define the energy distribution U. Planck approaches this problem using thermodynamic arguments related to ...