Physics 237, Midterm Exam #2

Tuesday April 14, 2009

12.30 pm – 1.45 pm

Do not turn the pages of the exam until you are instructed to do so.

Exam rules: You may use only a writing instrument and your equation sheet while taking this test. You may not consult any calculators, computers, books, or each other.

1. Problems 1 and 2 must be answered in booklet # 1.

2. Problems 3 and 4 must be answered in booklet # 2.

3. The answers need to be well motivated and expressed in terms of the variables used in the problem. You will receive partial credit where appropriate, but only when we can read your solution. Answers that are not motivated will not receive any credit, even if correct.

At the end of the exam, you need to hand in your exam, your equation sheet, and the two blue exam booklets. All items must be clearly labeled with your name, your student ID number, and the day/time of your workshop.

Name: __________________________________________________

ID number: ______________________________________________

Workshop Day/Time: ______________________________________

INTENTIONALLY LEFT BLANK

Problem 1 (35 points) ANSWER IN BOOKLET 1

Consider the lowest energy eigenfunctions for a one-electron atom, shown in the Table below.

a) What is the parity of the various y_3,2,m wavefunctions? Your answer needs to be well motivated.

b) Evaluate the electric dipole matrix element to determine whether transitions between the y_2,0,0 state and the y_1,0,0 state are possible.

c) Evaluate the electric dipole matrix element to determine whether transitions between the y_2,1,0 state and the y_1,0,0 state are possible.

Problem 2 (30 points) ANSWER IN BOOKLET 1

Measurements made on the line spectrum emitted by a certain atom of intermediate Z show that the ratio of the separation energies between three adjacent levels of increasing energy in a particular multiplet is approximately 3 to 5 (that is the energy difference between the 2^nd and the 3^rd member of the multiplet is 5/3 of the energy difference between the 1^st and the 2^nd member of the multiplet.)

a) What are the j’ quantum number that can be assigned to these states?

b) What is the s’ quantum number that can be assigned to these states?

c) What is the l’ quantum number that can be assigned to these states?

Problem 3 (30 points) ANSWER IN BOOKLET 2

A particle of mass m and energy is incident from the left on a potential

a) What is the wave function in the region x < 0? Note: you do no yet have to determine the value of the constants that appear in the wavefunction.

b) What is the wave function in the region 0 ≤ x ≤ L? Note: you do no yet have to determine the value of the constants that appear in the wavefunction.

c) What is the wave function in the region x > L? Note: you do no yet have to determine the value of the constants that appear in the wavefunction.

d) Calculate the reflection and transmission coefficients and show that their sum is equal to one.

Problem 4 (5 points) ANSWER IN BOOKLET 2

Back by popular demand! Please include the proper answer for part a and b in your exam booklet.

a) (2 points) Which of the following New York baseball teams are playing in a new baseball stadium this year?

1. Only the NY Yankees.

2. Only the NY Mets.

3. Both the NY Yankees and the NY Mets.

b) (3 points) This stadium is also known as (more than one answer may be correct)

1. The house that Ruth built.

2. Yankee stadium.

3. Fenway Park.

4. Frontier field.