Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The strong form of the Levinson theorem for a distorted KP potential   We present a heuristic derivation of the strong form of the Levinson theorem
for one-dimensional quasi-periodic potentials. The particular potential chosen
is a distorted Kronig-Penney model. This theorem relates the phase shifts of
the states at each band edge to the number of states crossing that edge, as the
system evolves from a simple periodic potential to a distorted one. By applying
this relationship to the two edges of each energy band, the modified Levinson
theorem for quasi-periodic potentials is derived. These two theorems differ
from the usual ones for isolated potentials in non-relativistic and
relativistic quantum mechanics by a crucial alternating sign factor $(-1)^{s}$,
where $s$ refers to the adjacent gap or band index, as explained in the text.
We also relate the total number of bound states present in each energy gap due
to the distortion to the phase shifts at its edges. At the end we present an
overall relationship between all of the phase shifts at the band edges and the
total number of bound states present.

13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat