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Chapter 6: Q2CQ (page 223)

For particles incident from the left on the potential energy shown below, what incident energies E would imply a possibility of later being found infinitely far to the right? Does your answer depend on whether the particles behave classically or quantum-mechanically?

Short Answer

Expert verified

The answer depends on the nature of particles: Quantum or Classical.

Step by step solution

01

Definition of tunneling

Classically, it is not allowed that a particle with energy less than the energy of a barrier would pass through it but quantum mechanically, it is possible. This phenomenon is called tunneling.

02

Explanation and conclusion

The solution to any energy greater than U1 would be sinusoidal. So, in the middle of the barrier to the right side, the transmission would be allowed.

But this would be possible only for a quantum particle. A classical particle would need energy greater than U2 to get past the barrier.

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Most popular questions from this chapter

A ball is thrown straight up at 25ms-1. Someone asks “Ignoring air resistance. What is the probability of the ball tunneling to a height of1000m?” Explain why this is not an example of tunneling as discussed in this chapter, even if the ball were replaced with a small fundamental particle. (The fact that the potential energy varies with position is not the whole answer-passing through nonrectangular barriers is still tunnelirl8.)

Calculate the reflection probability 5evfor an electron encountering a step in which the potential drop by 2ev

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What fraction of a beam of 50eVelectrons would get through a 200V1nm wide electrostatic barrier?

The plot below shows the variation of ω with k for electrons in a simple crystal. Where, if anywhere, does the group velocity exceed the phase velocity? (Sketching straight lines from the origin may help.) The trend indicated by a dashed curve is parabolic, but it is interrupted by a curious discontinuity, known as a band gap (see Chapter 10), where there are no allowed frequencies/energies. It turns out that the second derivative ofω with respect to k is inversely proportional to the effective mass of the electron. Argue that in this crystal, the effective mass is the same for most values of k, but that it is different for some values and in one region in a very strange way.
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