Physics 237, Midterm Exam #1

Tuesday February 20,
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: ____________________________________________________________________

**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)
(3 points) What
is the best baseball team in the USA

- Yankees.
- Mets.
- Red Sox.
- Buffalo
Bills
- AJAX

b)
(2 points) In
which country was the new 23-kg mass standard defined?

- The Netherlands.
- France.
- Germany.
- China.