Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Special rectangular (double-well and hole) potentials   We revisit a rectangular barrier as well as a rectangular well (pit) between
two rigid walls. The former is the well known double-well potential and the
latter is a hole potential. Let $|V_0|$ be the height (depth) of the barrier
(well) then for a fixed geometry of the potential, we show that in the
double-well, $E=V_0(>0)$, and in the hole potential ($V_0 <0$), $E=0$, can be
energy eigenvalues provided $V_0$ admits some special discrete values. These
states have been missed out earlier which emerge only when one seeks the
special zero-energy solution of one-dimensional Schr{\"o}dinger equation as
$\psi(x)=Bx+C$.

21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio