Learning Goal: To practice Problem-Solving Strategy 40.1 for quantum mechanics p

Question

Learning Goal:

To practice Problem-Solving Strategy 40.1 for quantum mechanics problems.

A particle of mass m in its first excited state is confined to a one-dimensional box of length L: an infinite square well, where the potential energy of a particle inside the box is zero, and the potential energy of a particle outside is infinite. Determine the probability PL/10 of finding the particle within L/10 from the center of the box.

Model

You are told that the particle is inside a one-dimensional box. This is a very simplified model that can be used to describe a more generic situation in which a particle is extremely well confined. You are also told that when the particle is inside the box, its potential energy is zero, and when the particle is outside the box, its potential energy is infinite. If the box is located on the x axis between x=0 and x=L, then the potential-energy function that describes the particle's interactions can be expressed as

U(x)=0 when 0?x?L

and

U(x)=? when x<0 and x>L.

PART A

First, draw the potential-energy curve for this problem. Then, identify known information. Your final graph might look like the picture shown to the left, where E is the total energy of the particle. (Figure 1)

Which of the following statements correctly describe the situation in this problem?

Enter the letter(s) corresponding to the correct statement(s) in alphabetical order. Do not use commas. For example, if you think that statements A, C, and D are correct, enter ACD.

PART B

Which of the following are the boundary conditions on the wave function ?(x) at positions x=0,L in this problem?

Enter the letter(s) of the correct answer(s) in alphabetical order. Do not use commas. For instance, if you think all but the last boundary condition are valid, enter ABC.

PART C

Explanation / Answer

Part B: AC

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.