Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nodal surfaces and interdimensional degeneracies   The aim of this paper is to shed light on the topology and properties of the
nodes (i.e. the zeros of the wave function) in electronic systems. Using the
"electrons on a sphere" model, we study the nodes of two-, three- and
four-electron systems in various ferromagnetic configurations ($sp$, $p^2$,
$sd$, $pd$, $p^3$, $sp^2$ and $sp^3$). In some particular cases ($sp$, $p^2$,
$sd$, $pd$ and $p^3$), we rigorously prove that the non-interacting wave
function has the same nodes as the exact (yet unknown) wave function. The
number of atomic and molecular systems for which the exact nodes are known
analytically is very limited and we show here that this peculiar feature can be
attributed to interdimensional degeneracies. Although we have not been able to
prove it rigorously, we conjecture that the nodes of the non-interacting wave
function for the $sp^3$ configuration are exact.

28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg