Abstract
For any finite group, an element (commutator Hamiltonian) is defined in its group algebra so that in any representation of that group the image of this element is diagonalizable and has the spectrum contained in the set {1/n 2|n = 1,2,3,…}. The result is generalized onto an arbitrary compact group. In particular, it is pointed out that for the natural representation of the group SU(2, C) in the space of complex-valued functions with the square of absolute values integrable over the Haar measure the multiplicity of the eigenvalue 1/n 2 of the commutator Hamiltonian is equal to n 2.
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References
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Original Russian Text © O.V.Gerasimova, 2008, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2008, Vol. 63, No. 6, pp. 71–74.
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Gerasimova, O.V. The spectrum of a commutator Hamiltonian is hydrogenlike. Moscow Univ. Math. Bull. 63, 273–276 (2008). https://doi.org/10.3103/S0027132208060090
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DOI: https://doi.org/10.3103/S0027132208060090