Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Path integrals and the double slit   Basic explanations of the double slit diffraction phenomenon include a
description of waves that emanate from two slits and interfere. The locations
of the interference minima and maxima are determined by the phase difference of
the waves. An optical wave, which has a wavelength ${\lambda}$ and propagates a
distance $L$, accumulates a phase of $2{\pi}L{/}{\lambda}$. A matter wave, also
having wavelength ${\lambda}$ and propagating the same distance $L$,
accumulates a phase of ${\pi}L{/}{\lambda}$, which is a factor of two different
from the optical case. Nevertheless, the phase difference, ${\Delta}{\phi}$,
for interfering matter waves that propagate distances that differ by
${\Delta}L$, is approximately $2{\pi}{\Delta}L{/}{\lambda}$, which is the same
value computed in the optical case. The difference between the matter and
optical case hinders conceptual explanations of diffraction from two slits
based on the matter-optics analogy. In the following article we provide a path
integral description for matter waves with a focus on conceptual explanation. A
thought experiment is provided to illustrate the validity range of the
approximation ${\Delta}{\phi}{\approx}2{\pi}{\Delta}L{/}{\lambda}$.

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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: math