\( \lambda = \frac hp = \frac {h}{mv} \)

The Davisson-Germer experiment proved beyond doubt the wave nature of matter by diffracting electrons through a crystal. In 1929, de Broglie was awarded the Noble prize for his matter wave theory and for opening up a whole new field of Quantum Physics. The matter wave theory was gracefully incorporated by the Heisenberg’s Uncertainty Principle. The Uncertainty Principle states that for an electron or any other particle, both the momentum and position cannot be known accurately at the same time. There is always some uncertainty with either the position ‘delta x’ or with the momentum, ‘delta p’. The Heisenberg’s Uncertainty equation is.

\( \sigma_x \sigma_p \le \frac {h}{2} \)

Say you measure the momentum of the particle accurately so that ‘delta p’ is zero. To satisfy the equation above, the uncertainty in the position of the particle, ‘delta x’ has to be infinite. From de Broglie’s equation, we know that a particle with a definite momentum has a definite wavelength ‘Lambda’. A definite wavelength extends all over space all the way to infinity. By Born’s Probability Interpretation this means that the particle is not localized in space and therefore the uncertainty of position becomes infinite. In real life though, the wavelengths have a finite boundary and are not infinite and thus both the position and momentum uncertainties have a finite value. De Broglie’s equation and Heisenberg’s Uncertainty Principle are apples of the same tree.

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