Uncertainty

# Uncertainty - negative and the total energy is conserved...

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Uncertainty A wave of sharp frequency has to last infinitely long, and is thus completely delocalised. What does this imply for matter waves? One of the implications is the uncertainty relation between position and momentum (1.9) This implies that the combined accuracy of a simultaneous measurement of position and momentum has a minimum. This is not important in problems on standard scales, for the Tunneling Figure 1.7: The tunneling phenomenon, where a particle can sometimes be found at the othee side of a barrier. In classical mechanics a billiard ball bounces back when it hits the side of the billiard. In the quantum world it might actually "tunnel" through. Let me make this a little clearer. Classically a particle moving in the following potential would just be bouncing back and fourth between the walls. This can be easily seen from conservation of energy: The kinetic energy can not go
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Unformatted text preview: negative, and the total energy is conserved. Where the potential is larger than the total energy, the particle cannot go. In quantum mechanics this is different, and particles can penetrate these classically forbidden regions, escaping from their cage. This is a wave phenomenon, and is related to the behaviour of waves in impenetrable media: rather than oscillatory solutions, we have exponentially damped ones, that allow for some penetration. This also occurs in processes such as total reflection of light from a surface, where the tunneling wave is called ``evanescent''. following practical reason. Suppose we measure the velocity of a particle of 1g to be m/s. In that case we can measure its position no more accurate that m, a completely outrageous accuracy (remember, this is times the atomic scale!)...
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## This note was uploaded on 11/09/2011 for the course PHY PHY2053 taught by Professor Davidjudd during the Fall '10 term at Broward College.

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