Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Parabolic Model for the Dimple Potentials   We study truncated parabolic function and demonstrate that it is a
representation of the Dirac delta function. We also show that the truncated
parabolic function, used as a potential in the Schr\"{o}dinger equation, has
the same bound state spectrum, tunneling and reflection amplitudes with the
Dirac delta potential as the width of the parabola approximates to zero. Dirac
delta potential is used to model dimple potentials which are utilized to
increase the phase-space density of a Bose-Einstein condensate in a harmonic
trap. We show that harmonic trap with a delta function at the origin is a limit
case of the harmonic trap with a symmetric truncated parabolic potential around
the origin. Therefore, we propose that the truncated parabolic potential is a
better candidate for modeling the dimple potentials.

26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex