Physics 237, Midterm Exam #2

Tuesday March 27, 2018

8.00 am Ð 9.30 am

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

Exam rules: You may use only a writing instrument while taking this test.  You may not consult any calculators, computers, books, nor each other.

Problems 1 and 2 must be answered in exam booklet 1.  Problems 3 and 4 must be answered in exam booklet 2.  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, the blue exam booklets, and the equation sheet.  All items must be clearly labeled with your name, your student ID number, and the day/time of your recitation.  If any of these items are missing, we will not grade your exam, and you will receive a score of 0 points.

You are required to complete the following Honor Pledge for Exams.  Copy and sign the pledge before starting your exam.

ÒI affirm that I will not give or receive any unauthorized help on this exam, and that all work will be my own.Ó

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Name:  ______________________________________________________________________

Signature:  ____________________________________________________________________

INTENTIONALLY LEFT BLANK

Problem 1 (35 points)                                                                        ANSWER IN BOOKLET 1

A particle of mass m and energy E, where

is incident from the left on a potential V:

a)     What is the wave function in the region x < 0?  Note: you do not yet have to determine the value of the constants that appear in the wavefunction.

b)    What is the wave function in the region 0 ² x ² L?  Note: you do not 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 not yet have to determine the value of the constants that appear in the wavefunction.

d)    Calculate the transmission coefficient.

Problem 2 (30 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 y3,2,m wavefunctions?  Your answer needs to be well motivated.

b)    Evaluate the electric dipole matrix element to determine whether transitions between the y2,0,0 state and the y1,0,0 state are possible.

Problem 3 (35 points)                                                                        ANSWER IN BOOKLET 2

Consider the ground-state wavefunctions of the Hydrogen atom, shown in the table below.

a)     What is the expectation value <V> of the potential energy of the hydrogen atom when it is in its ground state?

b)    Express the energy of the ground state of the hydrogen atom in terms of the expectation value <V> of the potential energy.

c)     What is the expectation value of the kinetic energy of the ground state?

Problem 4 (5 points)                                                                          ANSWER IN BOOKLET 2

a)     (2.5 points) What is the best airline in the world?

1. KLM.
2. United Airlines.
3. Singapore Airlines.
4. Cathay Pacific.
5. American Airlines.

b)    (2.5 points) What was the first airline in the world?

1.     KLM.

2.     United Airlines.

3.     Singapore Airlines.

4.     Cathay Pacific.

5.     American Airlines.