# Self-diagnostic test

Coming in to Stony Brook's graduate coursework can be a bit disorienting. The core courses are rather difficult for people who have not taken similar difficulty courses in the past, and so former students have compiled a set of characteristic questions from undergraduate textbooks that they believe give a taste of what you will be expected to have seen before.

The idea, to some extent, is that if you have significant difficulty understanding or solving these problems then you should schedule knowing that you will likely need to put extra effort into the respective core courses. Some people who are already comfortable with the core course materials are able to take 3 or 4 courses at once in the first semester, but this is often not very fun or healthy or academically advisable - **so if more than half of these questions are new ideas or highly non-trivial for you then please avoid doing too much in your first semesters.**

## Contents

## Self-diagnostic test to identify strengths and weaknesses before beginning PhD or Masters coursework

**PDF with all the questions listed provided here**

### Quantum Mechanics

- Sakurai Modern Quantum Mechanics (Second Edition) - Solutions
- Chapter 1 Problem 1 - Commutator Algebra
- Chapter 1 Problem 4 - Bra-ket Algebra
- Chapter 1 Problem 10 - Diagonalizing Hamiltonians
- Chapter 1 Problem 29 - Commutation Relations with Functions

- Griffiths Quantum Mechanics (Second Edition) - PhysicsPages.com Solutions
- Problem 2.14 - Simple Harmonic Oscillator
- Problem 7.1 - Variational Method

- Zettili Quantum Mechanics (Second Edition) - Steven Sagona's comprehensive exam study website has solutions, also Similar Solutions available in QM comprehensive exam resources
- Problem 5.5 - Spin Eigenstates

### Electromagnetism

- Jackson Electrodynamics (Third Edition) - Similar Solutions available in EM comprehensive exam resources
- Problem 1.1 - Basics
- Problem 2.1 - Method of Images
- Problem 5.33 - Mutual Inductance

- Griffiths Introduction to Electrodynamics (Fourth Edition) - PhysicsPages.com Solutions
- Problem 5.26 - Magnetic Vector Potentials
- Problem 7.37 - Maxwell's Equations

### Classical Mechanics

- Landau and Lifshitz Classical Mechanics (Third Edition) - Textbook
- Problem 1.1 - Double Pendulum
- Last question of chapter 2 section 7, page 16 - Conservation of Momentum

- Taylor Classical Mechanics (First Edition) - Similar Solutions available in CM comprehensive exam resources
- Problem 5.40 - Resonance
- Problem 11.4 - Normal Modes of Coupled Systems

- Goldstein Classical Mechanics (Third Edition) - Textbook
- Problem 3.19 - Orbital Motion
- Problem 8.15 - Hamiltonians and Lagrangians

### Statistical Mechanics

- Schroeder Introduction to Thermal Physics (Seventh Edition) - PhysicsPages.com Solutions, also Similar Solutions available in SM comprehensive exam resources
- Problem 3.10 - Entropy and Heat
- Problem 5.12 - Maxwell Relations
- Problem 6.45 - Derive everything from the Partition Function
- Problem 7.28 - Fermi Gas and Density of States
- Problem 7.72 - Bose Einstein Condensation