Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time Operators of Harmonic Oscillators and Their Representations I   A time operator of the one-dimensional harmonic oscillator $\hat
h_\epsilon=\frac{1}{2}(p^2+\epsilon q^2)$ is rigorously constructed. The time
operator is formally expressed as $\hat T_\epsilon=\frac{1}{2}\frac{1}{\sqrt
\epsilon } (\arctan \sqrt \epsilon \hat t+\arctan \sqrt \epsilon \hat t^\ast)$
with $\hat t=p^{-1}q$. It is shown that $[h_\epsilon, \hat T_\epsilon]=-i$ is
satisfied in the sense of sesquilinear form, and a representation of $\hat
T_\epsilon$ on a dense domain is given. Finally the limit of $\hat T_\epsilon $
as $\epsilon\to 0$ is shown.

37
The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics