Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum information measures of the Dirichlet and Neumann hyperspherical
  dots   $\mathtt{d}$-dimensional hyperspherical quantum dot with either Dirichlet or
Neumann boundary conditions (BCs) allows analytic solution of the
Schr\"{o}dinger equation in position space and the Fourier transform of the
corresponding wave function leads to the analytic form of its momentum
counterpart too. This paves the way to an efficient computation in either space
of Shannon, R\'{e}nyi and Tsallis entropies, Onicescu energies and Fisher
informations; for example, for the latter measure, some particular orbitals
exhibit simple expressions in either space at any BC type. A comparative study
of the influence of the edge requirement on the quantum information measures
proves that the lower threshold of the semi-infinite range of the dimensionless
R\'{e}nyi/Tsallis coefficient where one-parameter momentum entropies exist is
equal to $\mathtt{d}/(\mathtt{d}+3)$ for the Dirichlet hyperball and
$\mathtt{d}/(\mathtt{d}+1)$ for the Neumann one what means that at the
unrestricted growth of the dimensionality both measures have their Shannon
fellow as the lower verge. Simultaneously, this imposes the restriction on the
upper value of the interval $[1/2,\alpha_R)$ inside which the R\'{e}nyi
uncertainty relation for the sum of the position $R_\rho(\alpha)$ and wave
vector $R_\gamma\left(\frac{\alpha}{2\alpha-1}\right)$ components is defined:
$\alpha_R$ is equal to $\mathtt{d}/(\mathtt{d}-3)$ for the Dirichlet geometry
and to $\mathtt{d}/(\mathtt{d}-1)$ for the Neumann BC. Some other properties
are discussed from mathematical and physical points of view. Parallels are
drawn to the corresponding properties of the hydrogen atom and similarities and
differences are explained based on the analysis of the associated wave
functions.

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The categories of this paper are: adap-org
3
The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
18
The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg