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Chapter 40: Q. 15 (page 1175)

Sketch the n=1 and n=7 wave functions for the potential energy shown in FIGURE EX40.15

Short Answer

Expert verified

The sketch

Step by step solution

01

Step 1. Given information

For n=1, we have only one antinode, and most of the region is the classically forbidden region. So, before the node in the classically forbidden region, the wave function increases exponentially. After the node, the wave function decreases exponentially, as shown in the figure.

Forn=7, there are 7 nodes and 6 antinodes. There are classically forbidden regions before and after the nodes. The wavelength is large initially and then decreases and from the center of the well. The wavelength again increases the same way for amplitude.

02

Step 2. The sketch 

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Most popular questions from this chapter

An electron confined in a harmonic potential well emits a 1200nm photon as it undergoes a 3→2quantum jump. What is the spring constant of the potential well?

A 2.0μmdiameter water droplet is moving with a speed of 1.0mm/sin a 20μmlong box.

a. Estimate the particle’s quantum number.

b. Use the correspondence principle to determine whether quantum mechanics is needed to understand the particle’s motion or if it is “safe” to use classical physics.

An electron in a finite potential well has a 1.0nm penetration distance into the classically forbidden region. How far below U0 is the electron’s energy?

An electron is confined in a harmonic potential well that has a spring constant of 2.0 N/m. a. What are the first three energy levels of the electron? b. What wavelength photon is emitted if the electron undergoes a 3 S 1 quantum jump?

a. Determine the normalization constant A1for the n=1ground-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 n=1ground state will be found in the classically forbidden region.

c. (Optional) Use a numerical integration program to evaluate your probability expression of part b.
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