Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Wavefunctions from Energies: Applications in simple potentials   A remarkable mathematical property -- somehow hidden and recently
rediscovered -- allows obtaining the eigenvectors of a Hermitian matrix
directly from their eigenvalues. That opens the possibility to get the
wavefunctions from the spectrum, an elusive goal of many fields in physics.
Here, the formula is assessed for simple potentials, recovering the theoretical
wavefunctions within machine accuracy. A striking feature of this
eigenvalue--eigenvector relation is that it does not require knowing any of the
entries of the working matrix. However, it requires the knowledge of the
eigenvalues of the minor matrices (in which a row and a column have been
deleted from the original matrix). We found a pattern in these sub-matrices
spectra, allowing to get the eigenvectors analytically. The physical
information hidden behind this pattern is analyzed.

11
The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys