Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The partnership of potentials in Quantum Mechanics and Shape Invariance   The concept of partnership of potentials is studied in detail and in
particular the non-uniqueness due to the ambiguity in the election of the
factorization energy and in the choice of the solution of certain Riccati
equation. We generate new factorizations from old ones using invariance under
parameter transformations. The theory is illustrated with some examples.

21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
3
The categories of this paper are: physics
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex