Module 5 : MODERN PHYSICS
Lecture 23 : Black Body Radiation
Black Body Radiation :
\includegraphics{fig4.2.eps}
  Extending to three dimensions, the electric field is given by
 
$\displaystyle E = E_0\sin\left(n_x\frac{\pi}{L}x\right)\sin\left(n_y\frac{\pi}{L}y\right) \sin\left(n_z\frac{\pi}{L}z\right)\sin(\omega t)$
  where $ \{n_x,n_y,n_z\}$ is a set of positive integers. (If any of these inegers is zero, it gives zero field. Taking negative values of the integers do not give different fields as it amounts to simply multiplying $ E_0$ by a sign factor.) Substituting Eqn. (1) in the electromagnetic wave equation
 
$\displaystyle \nabla^2 E = \left( \frac{\partial^2}{\partial x^2} + \frac{\part... ...tial^2}{\partial z^2}\right)E = \frac{1}{c^2} \frac{\partial^2E}{\partial t^2}$
  we get
 
$\displaystyle \left(\frac{n_x^2\pi^2}{L^2}+ \frac{n_y^2\pi^2}{L^2}+ \frac{n_z^2\pi^2}{L^2} \right) E = \frac{\omega^2}{c^2}E$
 
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