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Chapter 40: Q. 31 (page 1176)
Show that the normalization constant for the wave functions of a particle in a rigid box has the value given in Equation 40.26.
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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?
a. Sketch graphs of the probability density for the four states in the finite potential well of Figure a. Stack them vertically, similar to the Figure a graph of .
b. What is the probability that a particle in the state of the finite potential well will be found at the center of the well? Explain.
c. Is your answer to part b consistent with what you know about standing waves? Explain.
Suppose that and are both solutions to the Schrödinger equation for the same potential energy . Prove that the superposition is also a solution to the Schrödinger equation.
A -long box has a thin partition that divides the box into a-long section and a-long section. An electron confined in the shorter section is in the state. The partition is briefly withdrawn, then reinserted, leaving the electron in the longer section of the box. What is the electron’s quantum state after the partition is back in place?
Four quantum particles, each with energy E, approach the potential-energy barriers seen in FIGURE Q40.8 from the left. Rank in order, from largest to smallest, the tunneling probabilities
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