Suggestions Wanted — How to create a Physics Problem Database?

by Jonathan Whitmore on 2010-12-12

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Physics graduate students at UCSD (and many other schools) have to pass a PhD qualifying exam. At UCSD, this exam is taken across 2 days. Taking and preparing for that exam (called The Qual) is often a stressful time of life.

One of the most useful ways to study for the Qual is to work through old qualifying exams. Graduate students have had access to the tests and the solutions stretching back to 1987. The tests are offered twice a year, so there are a fair number of questions to be solved out there. I have organized PDFs of each of the exams and what solutions can be found from the past Quals, but I was hoping to make the information more accessible and more useful.

The problems on the Qual are organized into several different categories. The first category is Undergraduate or Graduate problems. (The first day of the exam is Undergraduate, the second day is Graduate). Within those categories there are several subjects that are tested: Mechanics, Electricity & Magnetism, Statistical Mechanics, Quantum Mechanics, Mathematical Methods, and Miscellaneous. Other identifying features: Year, Season, and Problem number. So, for example.

2006 Spring #13

Graduate
Electricity & Magnetism

Problem: An electron is incident with impact parameter $\rho$ and speed $v_0$ on a proton at rest. Calculate the energy radiated during the collision assuming the ordering

$\displaystyle \frac{e^2}{\rho} \ll mv^2_o \ll mc^2$

Hint: this simplifies the orbit approximation.

Solution:

$\displaystyle F=ma=\frac{e^2}{r^2}$
$\displaystyle \left | \vec{a}\right |=\frac{e^2}{mr^2}\\$
$\displaystyle \left | \vec{a}\right |^2=\frac{e^4}{m^2r^4}\\$
$\displaystyle \ddot{\vec{p}}=e\ddot{\vec{r}}$
$\displaystyle \vec{a}=\ddot{\vec{r}}$
$\displaystyle P=\frac{2}{3}\frac{\left(\ddot{\vec{p}}\right)^2}{c^3}$

$\displaystyle P=\frac{2}{3}\frac{e^2}{c^3}\left | \vec{a}\right |^2=\frac{2}{3}\frac{e^6}{m^2r^4c^3}$

Energy radiated is $\displaystyle \int P \,dt$

$\displaystyle r^2=\rho^2+\left(v_o t\right)^2$

Since
$\displaystyle mv_o^2 \gg \frac{e^2}{\rho^2}$
$\displaystyle E=\frac{2}{3}\frac{e^6}{m^2c^3}\int_{- \infty }^{ \infty } \frac{1}{\left (\rho^2+\left (v_o t \right )^2\right)^2}\,dt$
$\displaystyle E=\frac{2}{3}\frac{e^6}{m^2c^3}\frac{1}{v_o\rho^4}\underbrace{\int_{- \infty }^{ \infty } \frac{1}{\left (1+x^2\right)^2}\,dx}_{\frac{\pi}{2}}$

Now, I think it would be very useful to be able to store the problem and solution and all the identifying pieces of information in a database in some way so that the following types of actions could be done.

Search and return all Electricity & Magnetism problems.
Search and return all graduate Statistical Mechanics problems.
Create a random qualifying exam — meaning a new 20 question test randomly picking 2 Undergrad mechanics problems, 2 Undergrade E&M problems, etc. from past qualifying exams (over some restricted date range).
Have the option to hide or display the solutions on results.

Any suggestions or comments on how best to do this project would be greatly appreciated!

Comments on this entry are closed.

West 2010-12-22, 17:50

Easiest way I've found is to set up three tables:

Questions

Categories

Relationships

Each question has an id (auto-incremented), question, answer, year, season, undergrad/grad, etc; basically, everything except the categories.

Categories is where you list all the possible categories, E&M, Stat Mech, etc. Each entry needs only an id and description ("Classical Mechanics").

The relationships table will have an id (probably won't use this, but it can sometimes be useful), question_id, and category_id.

This system lets you give questions multiple categories and add/remove categories at a future date without modifying your table structure (and probably breaking your code). Then to look up all questions with a specific category on the relationships table (and join it with the question table if necessary).

Displaying the random tests is an issue of what kind of categories you need, mix of grad/undergrad, and any date restrictions you want. You have all the data in the database; start with the most restrictive requirements and work outwards.

∞
Michael Folkerts 2012-07-21, 23:24

This is what I came up with: http://bit.ly/qualApp
Let me know if you need an account since you may not have your @physics.ucsd.edu e-mail anyomre.

∞

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