Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The eigenvalues and eigenfunctions of the toroidal dipole operator in a
  mesoscopic system   We give analytical expressions for the eigenvalues and generalized
eigenfunctions of $\hat{T}_3$, the $z$-axis projection of the toroidal dipole
operator, in a system consisting of a particle confined in a thin film bent
into a torus shape. We find the quantization rules for the eigenvalues, which
are essential for describing measurements of $\hat{T}_3$. The eigenfunctions
are not square-integrable, so they do not belong to the Hilbert space of wave
functions, but they can be interpreted in the formalism of rigged Hilbert
spaces as kernels of distributions. While these kernels appear to be
problematic at first glance due to singularities, they can actually be used in
practical computations. In order to illustrate this, we prescribe their action
explicitly and we also provide a normalization procedure.

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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: dg-ga