Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Galoisian Approach to integrability of Schr\"odinger Equation   In this paper, we examine the non-relativistic stationary Schr\"odinger
equation from a differential Galois-theoretic perspective. The main algorithmic
tools are pullbacks of second order ordinary linear differential operators, so
as to achieve rational function coefficients ("algebrization"), and Kovacic's
algorithm for solving the resulting equations. In particular, we use this
Galoisian approach to analyze Darboux transformations, Crum iterations and
supersymmetric quantum mechanics. We obtain the ground states, eigenvalues,
eigenfunctions, eigenstates and differential Galois groups of a large class of
Schr\"odinger equations, e.g. those with exactly solvable and shape invariant
potentials (the terms are defined within). Finally, we introduce a method for
determining when exact solvability is possible.

17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
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The categories of this paper are: eess
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph