rlm@0: #+TITLE: Bugs in Quantum Mechanics
rlm@0: #+AUTHOR: Dylan Holmes
rlm@0: #+SETUPFILE: ../../aurellem/org/setup.org
rlm@0: #+INCLUDE:   ../../aurellem/org/level-0.org
rlm@0: 
rlm@0: 
rlm@0: #Bugs in the Quantum-Mechanical Momentum Operator
rlm@0: 
rlm@0: 
rlm@0: I studied quantum mechanics the same way I study most subjects\mdash{}
rlm@0: by collecting (and squashing) bugs in my understanding. One of these
rlm@0: bugs persisted throughout two semesters of
rlm@0: quantum mechanics coursework until I finally found
rlm@0: the paper 
rlm@0: [[http://arxiv.org/abs/quant-ph/0103153][/Self-adjoint extensions of operators and the teaching of quantum
rlm@0: mechanics/]], which helped me stamp out the bug entirely. I decided to
rlm@0: write an article about the problem and its solution for a number of reasons:
rlm@0: 
rlm@0: - Although the paper was not unreasonably dense, it was written for
rlm@0:   teachers. I wanted to write an article for students.
rlm@0: - I wanted to popularize the problem and its solution because
rlm@0:   other explanations are currently too hard to find.
rlm@0: - I wanted to check that the bug was indeed entirely
rlm@0:   eradicated. Attempting an explanation is my way of making
rlm@0:   sure.
rlm@0: 
rlm@0: * COMMENT
rlm@0:  I recommend the
rlm@0: paper not only for students who are learning
rlm@0: quantum mechanics, but especially for teachers interested in debugging
rlm@0: them. 
rlm@0: 
rlm@0: * COMMENT
rlm@0: On my first exam in quantum mechanics, my professor asked us to
rlm@0: describe how certain measurements would affect a particle in a
rlm@0: box. Many of these measurement questions required routine application
rlm@0: of skills we had recently learned\mdash{}first, you recall (or
rlm@0: calculate) the eigenstates of the quantity
rlm@0: to be measured; second, you write the given state as a linear
rlm@0: sum of these eigenstates\mdash{} the coefficients on each term give
rlm@0: the probability amplitude.
rlm@0: 
rlm@0: * Statement of the Problem
rlm@0: A particle is 
rlm@0: 
rlm@0: 
rlm@0: 
rlm@0: 
rlm@0: * COMMENT [TABLE-OF-CONTENTS]