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Chapter 40: Q. 3 (page 1174)
A particle in a potential well is in the quantum state. How many peaks are in the probability density ?
There are five peaks in the probability density .
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An electron in a harmonic potential well absorbs a photon with a wavelength of as it undergoes a quantum jump. What wavelength is absorbed in a quantum jump?
FIGURE Qshows the de Broglie waves of three equal-mass particles. Which one is moving most slowly? Explain.
Two adjacent energy levels of an electron in a harmonic potential well are known to be and . What is the spring constant of the potential well?
Consider a particle in a rigid box of length L. For each of the states and :
a. Sketch graphs of . Label the points and .
b. Where, in terms of L, are the positions at which the particle is most likely to be found?
c. Where, in terms of L, are the positions at which the particle is least likely to be found?
d. Determine, by examining your graphs, if the probability of finding the particle in the left one-third of the box is less than, equal to, or greater than . Explain your reasoning.
e. Calculate the probability that the particle will be found in the left one-third of the box
For the quantum-well laser of Figure 40.16, estimate the probability that an electron will be found within one of the GaAlAs layers rather than in the GA As layer. Explain your reasoning.
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