Module 6 : PHYSICS OF SEMICONDUCTOR DEVICES
Lecture 30 : Quantum Mechanical Concepts
Quantum Mechanical Concepts
Formation of bands can only be understood on the basis of quantum mechanics. Earlier, we had seen that an object behaves both as particle and as wave. According to de Broglie theory, an electron having a momentum $ p$ has an associated wave with a wavelength $ h/p$. Schrödinger proposed an equation for the wave associated with a particle of mass $ m$ having a total energy $ E$ which is moving in a potential $ V$. The Schrödinger equation, which is as fundamental to quantum mechanics as Newton's laws are to classical mechanics, is given by
 
$\displaystyle -\frac{\hbar^2}{2m}\nabla^2\psi = (E-V)\psi$
  According to quantum mechanical hypothesis, the wavefunction is interpreted as the probability amplitude of a particle of energy $ E$ being at a point $ \vec r$. The square of the wavefunction $ \mid\psi(\vec r)\mid^2$ gives the probability density at the point, so that the probability of finding the particle anywhere in space given by $ \int_{\rm all\ space} \mid\psi(\vec r)\mid^2 d^3r$ is unity. This is called the normalization of the wavefunction. It is also postulated that the wavefunction and its first derivative are continuous and single valued.
   
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