9 Oscillator representations for self - adjoint Calogero Hamiltonians
نویسنده
چکیده
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) = αx−2. In such a way, we have described all possible s.a. operators (s.a. Hamiltonians) associated with the formal differential expression Ȟ = −dx + αx−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 N̂ = â+â and  = ââ+ are called operators of oscillator type. Oscillator type operators obey several useful properties in case if the elementary operator â and â+ 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.
منابع مشابه
9 Self - adjoint extensions and spectral analysis in Calogero problem
In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential αx−2 . Although the problem is quite old and well-studied, we believe that our consideration, based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in o...
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