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Chapter 40: Q. 11 (page 1175)
An electron in a finite potential well has a penetration distance into the classically forbidden region. How far below is the electron’s energy?
The energy is below the
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An electron in a rigid box absorbs light. The longest wavelength in the absorption spectrum is. How long is the box?
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
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.
Verify that the n=1 wave function of the quantum harmonic oscillator really is a solution of the Schrödinger equation. That is, show that the right and left sides of the Schrödinger equation are equal if you use the wave function.
The graph in FIGURE EX40.16 shows the potential-energy function U(x of a particle. Solution of the Schrödinger equation finds that the n=3 level has and that the n=6 level has .
a. Redraw this figure and add to it the energy lines for the n=3 and n=6 states.
b. Sketch the n=3 and n=6 wave functions. Show them as oscillating about the appropriate energy line.
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