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1 #+TITLE: Bugs in Quantum Mechanics
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2 #+AUTHOR: Dylan Holmes
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3 #+SETUPFILE: ../../aurellem/org/setup.org
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4 #+INCLUDE: ../../aurellem/org/level-0.org
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5
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6
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7 #Bugs in the Quantum-Mechanical Momentum Operator
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8
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9
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10 I studied quantum mechanics the same way I study most subjects\mdash{}
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11 by collecting (and squashing) bugs in my understanding. One of these
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12 bugs persisted throughout two semesters of
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13 quantum mechanics coursework until I finally found
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14 the paper
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15 [[http://arxiv.org/abs/quant-ph/0103153][/Self-adjoint extensions of operators and the teaching of quantum
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16 mechanics/]], which helped me stamp out the bug entirely. I decided to
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17 write an article about the problem and its solution for a number of reasons:
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18
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19 - Although the paper was not unreasonably dense, it was written for
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20 teachers. I wanted to write an article for students.
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21 - I wanted to popularize the problem and its solution because
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22 other explanations are currently too hard to find.
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23 - I wanted to check that the bug was indeed entirely
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24 eradicated. Attempting an explanation is my way of making
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25 sure.
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26
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27 * COMMENT
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28 I recommend the
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29 paper not only for students who are learning
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30 quantum mechanics, but especially for teachers interested in debugging
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31 them.
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32
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33 * COMMENT
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34 On my first exam in quantum mechanics, my professor asked us to
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35 describe how certain measurements would affect a particle in a
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36 box. Many of these measurement questions required routine application
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37 of skills we had recently learned\mdash{}first, you recall (or
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38 calculate) the eigenstates of the quantity
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39 to be measured; second, you write the given state as a linear
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40 sum of these eigenstates\mdash{} the coefficients on each term give
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41 the probability amplitude.
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42
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43 * Statement of the Problem
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44 A particle is
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45
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46
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47
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48
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49 * COMMENT [TABLE-OF-CONTENTS]
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