Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New exact solutions for polynomial oscillators in large dimensions   A new type of exact solvability is reported. We study the general central
polynomial potentials (with 2q anharmonic terms) which satisfy the Magyari's
partial exact solvability conditions (this means that they possess a
harmonic-oscillator-like wave function proportional to a polynomial of any
integer degree N). Working in the space of a very large dimension D for
simplicity, we reveal that in contrast to the usual version of the model in
finite dimensions (requiring a purely numerical treatment of the Magyari's
constraints), our large D problem acquires an explicit, closed form solution at
all N and up to q = 5 at least. This means that our effective secular
polynomials (generated via the standard technique of Groebner bases) happen to
be all fully factorizable in an utterly mysterious manner (mostly, over
integers).

16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph