Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Exact Solution to the Schr\"{o}dinger Equation with the Octic
  Potential   The Schr\"{o}dinger equation with the central potential is first studied in
the arbitrary dimensional spaces and obtained an analogy of the two-dimensional
Schr\"{o}dinger equation for the radial wave function through a simple
transformation. As an example, applying an ${\it ansatz}$ to the
eigenfunctions, we then arrive at an exact closed form solution to the modified
two-dimensional Schr\"{o}dinger equation with the octic potential,
$V(r)=ar^2-br^4+cr^6-dr^4+er^{10}$.

12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex