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Tunneling Example 2

Tunneling is the quantum mechanical phenomenon where a particle moves through a potential barrier that it classically could not surmount. A classic example of tunneling is the passage of a classical electron through the potential barrier formed by the edges of a square potential well. Quantum mechanically, tunneling can be understood using the Heisenberg uncertainty principle and the wave–particle duality of matter. Tunneling is commonly observed in atomic, molecular, and solid-state systems. Tunneling is of particular importance in the field of quantum computing, and is the mechanism responsible for the quantum tunnelling effect, a process by which a particle tunnels through a barrier that it classically would not be able to surmount.

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Video Transcript

welcome to our second example video. Looking at finite potential wells in this video, we're going to consider the probability of a tunneling event. Given that we have the same energy is we just calculated 1.26 TV for 1.3. Evey potential well will say that the width of our barrier is one nanometer. Given this, we can plug it into our probability equation of E to the negative to W Times Kappa, where Kappa is equal to this constant. Over here, you can go ahead and plug things in and then calculate. I recommend again that you try it, make sure you're doing things right. With your units, you should get a probability of 0.13 or rather 13% when you do it for one nanometer barrier. And if you do it for a two nanometer barrier, you would end up with 20.16 or 1.6% so you can see increasing that distance here makes a big change in the probability or whether of whether or not it's going to happen. It's already not very likely with a one nanometer barrier. It's even less likely if it gets any thicker

RC
University of North Carolina at Chapel Hill
Top Physics 103 Educators
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Liev B.

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