Chapter 6: Q5CQ (page 223)
Your friend has just finished classical physics and can’t wait to know what lies ahead. Keeping extraneous ideas and postulates to a minimum, Explain the process of Quantum-mechanical tunneling.
Whatever you have studied under classical physics is forbidden, is allowed quantum-mechanically.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
A ball is thrown straight up at . Someone asks “Ignoring air resistance. What is the probability of the ball tunneling to a height of?” 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.)
For the E>U0 potential barrier, the reflection, and transmission probabilities are the ratios:
Where A, B, and F are multiplicative coefficients of the incident, reflected, and transmitted waves. From the four smoothness conditions, solve for B and F in terms of A, insert them in R and T ratios, and thus derive equations (6-12).
The diagram below plots ω(k) versus wave number for a particular phenomenon. How do the phase and group velocities compare, and do the answer depend on the central value of k under consideration? Explain.
Show that the quite general wave group given in equation (6-21) is a solution of the free-particle Schrödinger equation, provided that each plane wave's w does satisfy the matter-wave dispersion relation given in (6-23).
Show that if you attempt to detect a particle while tunneling, your experiment must render its kinetic energy so uncertain that it might well be "over the top."
What do you think about this solution?
We value your feedback to improve our textbook solutions.
