Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modification of Crum's Theorem for `Discrete' Quantum Mechanics   Crum's theorem in one-dimensional quantum mechanics asserts the existence of
an associated Hamiltonian system for any given Hamiltonian with the complete
set of eigenvalues and eigenfunctions. The associated system is iso-spectral to
the original one except for the lowest energy state, which is deleted. A
modification due to Krein-Adler provides algebraic construction of a new
complete Hamiltonian system by deleting a finite number of energy levels. Here
we present a discrete version of the modification based on the Crum's theorem
for the `discrete' quantum mechanics developed by two of the present authors.

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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: econ
30
The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: physics