Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extensions of the auxiliary field method to solve Schr\"{o}dinger
  equations   It has recently been shown that the auxiliary field method is an interesting
tool to compute approximate analytical solutions of the Schr\"{o}dinger
equation. This technique can generate the spectrum associated with an arbitrary
potential $V(r)$ starting from the analytically known spectrum of a particular
potential $P(r)$. In the present work, general important properties of the
auxiliary field method are proved, such as scaling laws and independence of the
results on the choice of $P(r)$. The method is extended in order to find
accurate analytical energy formulae for radial potentials of the form $a
P(r)+V(r)$, and several explicit examples are studied. Connections existing
between the perturbation theory and the auxiliary field method are also
discussed.

23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol