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author Robert McIntyre <rlm@mit.edu>
date Fri, 28 Oct 2011 00:06:37 -0700
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1 #+TITLE: Bugs in Quantum Mechanics
2 #+AUTHOR: Dylan Holmes
3 #+SETUPFILE: ../../aurellem/org/setup.org
4 #+INCLUDE: ../../aurellem/org/level-0.org
5
6
7 #Bugs in the Quantum-Mechanical Momentum Operator
8
9
10 I studied quantum mechanics the same way I study most subjects\mdash{}
11 by collecting (and squashing) bugs in my understanding. One of these
12 bugs persisted throughout two semesters of
13 quantum mechanics coursework until I finally found
14 the paper
15 [[http://arxiv.org/abs/quant-ph/0103153][/Self-adjoint extensions of operators and the teaching of quantum
16 mechanics/]], which helped me stamp out the bug entirely. I decided to
17 write an article about the problem and its solution for a number of reasons:
18
19 - Although the paper was not unreasonably dense, it was written for
20 teachers. I wanted to write an article for students.
21 - I wanted to popularize the problem and its solution because
22 other explanations are currently too hard to find.
23 - I wanted to check that the bug was indeed entirely
24 eradicated. Attempting an explanation is my way of making
25 sure.
26
27 * COMMENT
28 I recommend the
29 paper not only for students who are learning
30 quantum mechanics, but especially for teachers interested in debugging
31 them.
32
33 * COMMENT
34 On my first exam in quantum mechanics, my professor asked us to
35 describe how certain measurements would affect a particle in a
36 box. Many of these measurement questions required routine application
37 of skills we had recently learned\mdash{}first, you recall (or
38 calculate) the eigenstates of the quantity
39 to be measured; second, you write the given state as a linear
40 sum of these eigenstates\mdash{} the coefficients on each term give
41 the probability amplitude.
42
43 * Statement of the Problem
44 A particle is
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48
49 * COMMENT [TABLE-OF-CONTENTS]