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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.
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Jump to JupiterThe gravitational potential energy of a 1kg object is plotted versus position from Earth’s surface to the surface of Jupiter. Mostly it is due to the two planets.
Make the crude approximation that this is a rectangular barrier of widthm and approximate height of. Your mass is 65 kg, and you launch your-self from Earth at an impressive 4 m/s. What is the probability that you can jump to Jupiter?
For wavelengths greater than about, the dispersion relation for waves on the surface of water is
(a) Calculate the phase and group velocities for a wave ofwavelength.
(b) Will the wave spread as it travels? Justify your answer.
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).
Example 6.3 gives the refractive index for high-frequency electromagnetic radiation passing through Earth’s ionosphere. The constant , related to the so-called plasma frequency, varies with atmospheric conditions, but a typical value is . Given a GPS pulse of frequency traveling through of ionosphere, by how much, in meters, would the wave group and a particular wave crest be ahead of or behind (as the case may be) a pulse of light passing through the same distance of vacuum?
Suppose the tunneling probability isfor a wide barrier when E is
(a) About how much smaller would it be if ’E’ were instead ?
(b) If this case does not support the general rule that transmission probability is a sensitive function of E, what makes it exceptional?
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