Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete supersymmetries of the Schrodinger equation and non-local
  exactly solvable potentials   Using an isomorphism between Hilbert spaces $L^2$ and $\ell^{2}$ we consider
Hamiltonians which have tridiagonal matrix representations (Jacobi matrices) in
a discrete basis and an eigenvalue problem is reduced to solving a three term
difference equation. Technique of intertwining operators is applied to creating
new families of exactly solvable Jacobi matrices. It is shown that any thus
obtained Jacobi matrix gives rise to a new exactly solvable non-local potential
of the Schroedinger equation. We also show that the algebraic structure
underlying our approach corresponds to supersymmetry. Supercharge operators
acting in the space $\ell^{2}\times \ell^{2} $ are introduced which together
with a matrix form of the superhamiltonian close the simplest superalgebra.

17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics