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---
layout: default
---
<a id="main"></a>
<h1>Phys622 — Graduate Quantum Mechanics II</h1>
<br>
<!-- ============================================== -->
<h3>Purpose of this course</h3>
<p> This is the second semester of the two semester 621/622
cycle. Building upon our progress last semester, we will explore
more advanced techniques and applications of quantum mechanics.
</p>
<!-- ============================================== -->
<h3>Class Schedule</h3>
<p>Tuesdays and Thursdays, 11am — 12.20pm in Small Hall 122.</p>
<!-- ============================================== -->
<h3>Office Hours</h3>
<p>Tuesdays and Thursdays, 2pm — 3pm in my office.</p>
<!-- ============================================== -->
<h3>Midterm Exam</h3>
<p>Thursday March 21st during class time.</p>
<!-- ============================================== -->
<h3>Final Exam</h3>
<p>Tuesday May 14th, 2pm in usual classroom.</p>
<!-- ============================================== -->
<h3>Lecture Notes</h3>
<p>I’ll post lecture notes on this website as we go along, which will sometimes contain a bit more information than we cover during lecture time. Hopefully this means you can do less writing and be a bit more focussed during lecture time. Please let me know of any errors you spot in the notes.</p>
<!-- ============================================== -->
<h3>Problem Sets</h3>
<p>There will be regular problem sets on the material we cover in lectures. These are a very important part of the course, almost certainly more important than listening to your lecturer waffle on. Sitting through lectures may make you <i>feel</i> like you have learned something, but you don’t really know until you try to use the techniques you think you have learned.</p>
<p>I will try my best to make the problems pedagogic so that you learn something by doing them. You should attempt the problems first on your own, but if you find you can’t solve a problem, you should seek help, either from me, or by collaborating with your classmates. But it is important that what you submit at the end represents <i>your</i> understanding of the problem — simply copying someone else's solution without understanding it is cheating and will not be tolerated.</p>
<p>You should try to present your solutions 'professionally' — they should feature text explaining what each major step in your solution is trying to do, and labelling any prior results you are making use of. I’ll provide my own solutions each week so you can get a better idea of what I mean. You don’t need to use LaTeX or other typesetting (unless you want to), but I do need to be able to read what you submit, so please think about legibility.</p>
<p>I want to emphasize that problems sets are not meant primarily as an assessment exercise, and for that reason, relatively little grade-credit is assigned to them. The payoff for putting in the effort comes in the form of learning, and the grade payoff comes when you get high grades in the midterm and the final exam, because you are so well-prepared, and then ace the QM problems on the qualifier.</p>
<p>The problem sets and deadlines are posted below.</p>
<!-- ============================================== -->
<h3>Books</h3>
<p>There is no single recommended QM book for this class. There is a
huge range to choose from, and you should select one which best
matches your preparation</p>
<ul>
<li>Sakurai <i>Modern Quantum Mechanics</i>. Newer editions have
been updated by Jim Napolitano. A nice and relatively short book at
the graduate level. Clear notation, nice problems, but not a huge
consideration of 'applications', and relatively little on wave
equations. Probably the best choice for most students.</li>
<li>Gottfried & Yan <i>Quantum Mechanics: Fundamentals</i>. Gets through
the basic material quite quickly, more formal in some places, but
quite a few nice applications. Assumes more math confidence than
Sakurai. More typos that you might like, but most of them are listed
on a website.</li>
<li>Landau & Lifshitz <i>Quantum Mechanics (Non-relativistic
theory)</i>. Hardcore, assumes you are a master of mathematics. But
very thorough, and well written / translated from Russian. Notation
may take some getting used to.</li>
</ul>
<p>There are loads of other good books that I just don’t happen to know well, so find one that works for you. Most textbooks will say in the authors' foreword if they are aimed at the graduate level, and generally they all contain the same core topics. I would strongly recommend you do have at least one textbook on hand, and that you read the relevant sections in parallel as we go through the course.</p>
<!-- ============================================== -->
<h3>Math</h3>
<p>As in Phys621, mainly linear algebra, simple solution of
differential equations, and, of increasing importance in this second semester, complex
variable theory.</p>
<!-- ============================================== -->
<h3>Topics</h3>
<ul>
<li>Coupling angular momentum</li>
<li>Tensor operators and the Wigner-Eckart theorem</li>
<li>Variational methods</li>
<li>Perturbation theory</li>
<li>Time-dependent perturbation theory</li>
<li>Systems of identical particles</li>
<li>Scattering in three-dimensions</li>
<li>Attempts at relativistic quantum mechanics</li>
</ul>
<!-- ============================================== -->
<h3>Grading</h3>
<p> Problem Sets: <i>30%</i>, Midterm Exam: <i>25%</i>, Final Exam: <i>45%</i>. </p>
<!-- ============================================== -->
<h3>Lecture Notes</h3>
<table class="highlights">
<tr class="highlights">
<td class="highlights"> 1. </td>
<td class="highlights">Coupling angular momentum</td>
<td class="highlights">
<a href="https://wm1693.box.com/s/hmao52kt0t8j3g31mbc47we2h2ry4dgs">[pdf]</a>
</td>
</tr>
<tr class="highlights">
<td class="highlights"> 2. </td>
<td class="highlights">Tensor operators</td>
<td class="highlights">
<a href="https://wm1693.box.com/s/grw04fcwel353kui9phutka8t6pdbmk0">[pdf]</a>
</td>
</tr>
<tr class="highlights">
<td class="highlights"> 3. </td>
<td class="highlights">Variational methods</td>
<td class="highlights">
<a href="https://wm1693.box.com/s/homm5q4v9xf1xf59wizff6k23723rjsk">[pdf]</a>
</td>
</tr>
<tr class="highlights">
<td class="highlights"> 4. </td>
<td class="highlights">Time-independent perturbation theory</td>
<td class="highlights">
<a href="https://wm1693.box.com/s/mv038k5vsggohwlqw9rz285quq1ozw3k">[pdf]</a>
</td>
</tr>
<tr class="highlights">
<td class="highlights"> 5. </td>
<td class="highlights">Time-dependent perturbation theory</td>
<td class="highlights">
<a
href="https://wm1693.box.com/s/mmm9xv1ryxi8u6jn8ql1aoj7hdqo4m6z">[pdf]</a>
<a href="https://wm1693.box.com/s/5gzffvqoswbm8xw2ifbumdly1c9vujuu">[pdf2]</a>
</td>
</tr>
<tr class="highlights">
<td class="highlights"> 6. </td>
<td class="highlights">Systems of identical particles</td>
<td class="highlights">
<a
href="https://wm1693.box.com/s/u0avboe9nhqg354xvr69xderxcsnbtt3">[pdf]</a>
<a href="https://wm1693.box.com/s/0n0e78rxo1rdwsdwk4qswoy9n5imz1fm">[pdf2]</a>
</td>
</tr>
<tr class="highlights">
<td class="highlights"> 7. </td>
<td class="highlights">Scattering in three-dimensions</td>
<td class="highlights">
<a href="https://wm1693.box.com/s/s136x03trqcegl0z2r1vt2ex2le86a90">[pdf]</a>
</td>
</tr>
<tr class="highlights">
<td class="highlights"> 8. </td>
<td class="highlights">Attempts at relativistic quantum mechanics</td>
<td class="highlights">
<a href="https://wm1693.box.com/s/gin7fzlmrddx973acwyrwdxg0bl6cgr3">[pdf]</a>
</td>
</tr>
</table>
<!-- ============================================== -->
<br>
<h3>Problem Sets</h3>
<table class="highlights">
<tr class="highlights">
<td class="highlights"> 1. </td>
<td class="highlights">Coupling angular momentum</td>
<td class="highlights">
<a href="https://wm1693.box.com/s/s8rqn7grdw07929d8uvqkwi8j0svv8bj">[pdf]</a>
</td>
<td class="highlights">due Feb. 9</td>
</tr>
<tr class="highlights">
<td class="highlights"> 2. </td>
<td class="highlights">Tensor operators</td>
<td class="highlights">
<a href="https://wm1693.box.com/s/02uf305lqs4evoh30j4j5kgd1uvbn2ry">[pdf]</a>
</td>
<td class="highlights">due Feb. 16</td>
</tr>
<tr class="highlights">
<td class="highlights"> 3. </td>
<td class="highlights">Variational methods</td>
<td class="highlights">
<a href="https://wm1693.box.com/s/b5zzbdvffxd4j4s4pxv8lh7jf04a679o">[pdf]</a>
</td>
<td class="highlights">due Feb. 23</td>
</tr>
<tr class="highlights">
<td class="highlights"> 4. </td>
<td class="highlights">Perturbation theory</td>
<td class="highlights">
<a href="https://wm1693.box.com/s/iotjo7sarw48gh2w7p75u0w8qysq2604">[pdf]</a>
</td>
<td class="highlights">due Mar. 1</td>
</tr>
<tr class="highlights">
<td class="highlights"> 5. </td>
<td class="highlights">Time-dependence</td>
<td class="highlights">
<a href="https://wm1693.box.com/s/gij9whft69pkal0m3t2p6pd8gww4fkjk">[pdf]</a>
</td>
<td class="highlights">due Mar. 19</td>
</tr>
<tr class="highlights">
<td class="highlights"> 6. </td>
<td class="highlights">Identical particles</td>
<td class="highlights">
<a href="https://wm1693.box.com/s/b1al156px79sw89pxzvpaa4hraluzut8">[pdf]</a>
</td>
<td class="highlights">due Mar. 29</td>
</tr>
<tr class="highlights">
<td class="highlights"> 7. </td>
<td class="highlights">Scattering 1</td>
<td class="highlights">
<a href="https://wm1693.box.com/s/w4lf7y96kexq6gnjlaxrhrsbg9xsbdko">[pdf]</a>
</td>
<td class="highlights">due Apr. 19</td>
</tr>
<tr class="highlights">
<td class="highlights"> 8. </td>
<td class="highlights">Scattering 2</td>
<td class="highlights">
<a href="https://wm1693.box.com/s/ju2m2mfop32ceuz80s5fqfijrm5m9z0d">[pdf]</a>
</td>
<td class="highlights">due May. 3</td>
</tr>
</table>
</div>