Mercurial > dylan

     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 

    45 

    46 

    47 

    48 

    49 * COMMENT [TABLE-OF-CONTENTS]
author	Robert McIntyre <rlm@mit.edu>
date	Mon, 17 Oct 2011 23:17:55 -0700
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