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

_____________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

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 *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.

**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**

Please include the proper answer for
part a and b in your exam booklet.

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

- KLM.
- United
Airlines.
- Singapore
Airlines.
- Cathay
Pacific.
- 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.