Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solvable models of an open well and a bottomless barrier in 1-D   We present one dimensional potentials $V(x)= V_0[e^{2|x|/a}-1]$ as solvable
models of a well $(V_0>0)$ and a barrier ($V_0<0$). Apart from being new
addition to solvable models, these models are instructive for finding bound and
scattering states from the analytic solutions of Schr{\"o}dinger equation. The
exact analytic (semi-classical and quantal) forms for bound states of the well
and reflection/transmission $(R/T)$ co-efficients for the barrier have been
derived. Interestingly, the crossover energy $E_c$ where $R(E_c)=1/2=T(E_c)$
may occur below/above or at the barrier-top. A connection between poles of
these co-efficients and bound state eigenvalues of the well has also been
demonstrated.

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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: math
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom