Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From self-adjoint to non self-adjoint harmonic oscillators: physical
  consequences and mathematical pitfalls   Using as a prototype example the harmonic oscillator we show how losing
self-adjointness of the hamiltonian $H$ changes drastically the related
functional structure. In particular, we show that even a small deviation from
strict self-adjointness of $H$ produces two deep consequences, not well
understood in the literature: first of all, the original orthonormal basis of
$H$ splits into two families of biorthogonal vectors. These two families are
complete but, contrarily to what often claimed for similar systems, none of
them is a basis for the Hilbert space $\Hil$. Secondly, the so-called metric
operator is unbounded, as well as its inverse.
  In the second part of the paper, after an extension of some previous results
on the so-called $\D$ pseudo-bosons, we discuss some aspects of our extended
harmonic oscillator from this different point of view.

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The categories of this paper are: hep-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin