Physics 237, Midterm Exam #1

Tuesday February 21,
2012

8.00 am – 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.

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: ______________________________________

**Problem 1
(30 points) ANSWER
IN BOOKLET 1**

Consider a particle with charge *e* and rest mass *m*_{0}. The particle is accelerated to
relativistic speeds by an accelerating potential *V*.

a)
What is the de
Broglie wavelength of this particle as function of *V*?

b)
Show that the
expression obtained in a) is consistent with assumption de Broglie made in the
non-relativistic limit expressed in terms of the rest mass of the particle and
its velocity.

**Problem 2
(30 points) ANSWER
IN BOOKLET 1**

The
Wilson-Sommerfeld quantization rule states that

*For any
physics system in which the coordinates are periodic functions of time, there
exists a quantum condition for each coordinate. These quantum conditions are*

*where q is
the one of the coordinates, p _{q} is the momentum associated with that
coordinate, n_{q} is a quantum numbers which taken on integral values,
and means that the integration is taken over one period of
the coordinate q.*

a)
Show how the
Bohr quantization of angular momentum follows from the Wilson-Summerfeld rule.

b)
Show how
PlanckÕs quantization law follows from the Wilson-Summerfeld rule.

Note:
the area of the ellipse *x*^{2}*/*a^{2} + *y*^{2}/*b*^{2}
= 1 is *¹ab*.

**Problem 3
(35 points) ANSWER
IN BOOKLET 2**

The
energy of a linear harmonic oscillator is equal to . The
angular frequency of this oscillator is .

a)
Show, using the
uncertainty relations, that the energy of the linear harmonic oscillator can be
written as

b)
Show that the
minimum energy of the oscillator is *hv*/2
where

**Problem 4 (5 points) ANSWER
IN BOOKLET 2**

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 have moved from their old stadiums
into new stadiums during the last four years?

- Only the
NY Yankees.
- Only the
NY Mets.
- Both the
NY Yankees and the NY Mets.

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

- The
house that Ruth built.
- Yankee
stadium.
- Fenway
Park.
- Frontier
field.