Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large Oscillator representations for self-adjoint Calogero Hamiltonians   In the article arXiv:0903.5277 [quant-ph], we have presented a mathematically
rigorous quantum-mechanical treatment of a one-dimensional motion of a particle
in the Calogero potential $V(x)=\alpha x^{-2}$. In such a way, we have
described all possible s.a. operators (s.a. Hamiltonians) associated with the
formal differential expression $\check{H}=-d_{x}^{2}+\alpha x^{-2}$ for the
Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the
so-called oscillator representation for the Calogero Hamiltonians. As it is
know, operators of the form $\hat{N}=\hat{a}^{+}\hat{a}$ and
$\hat{A}=\hat{a}\hat{a}^{+}$ are called operators of oscillator type.
Oscillator type operators obey several useful properties in case if the
elementary operator $\hat{a}$ and $\hat{a}^{+}$ are densely defined. It turns
out that some s.a. Calogero Hamiltonians are oscillator type operators. We
describe such Hamiltonians and find the corresponding mutually adjoint
elementary operators.

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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con