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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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FIGURE EX is the probability density for an electron in a rigid box. What is the electron’s energy, in ?
The energy of an electron in a deep potential well is . At what distance into the classically forbidden region has the amplitude of the wave function decreased to of its value at the edge of the potential well?
a. Determine the normalization constant for the ground-state wave function of the quantum harmonic oscillator. Your answer will be in terms of b.
b. Write an expression for the probability that a quantum harmonic oscillator in its ground state will be found in the classically forbidden region.
c. (Optional) Use a numerical integration program to evaluate your probability expression of part b.
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.
An electron approaches a wide potential-energy barrier of height . What energy electron has a tunneling probability of (a) 10%, (b) 1.0%, and (c) 0.10%?
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