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Infinite family of superintegrable quantum Hamiltonians on a plane generalizing the Calogero-Marchioro-Wolfes model | | C. Quesne
; | | Date: |
23 Nov 2009 | | Abstract: | In a recent FTC by Tremblay {sl et al} (2009 {sl J. Phys. A: Math. Theor.}
{f 42} 205206), it has been conjectured that for any integer value of $k$,
some novel exactly solvable and integrable quantum Hamiltonian $H_k$ on a plane
is superintegrable and that the additional integral of motion is a $2k$th-order
differential operator $Y_{2k}$. Here we demonstrate the conjecture for the
infinite family of Hamiltonians $H_k$ with odd $k ge 3$, generalizing the
three-body Calogero-Marchioro-Wolfes model after eliminating the centre-of-mass
motion from the latter. Our approach is based on the construction of some
$D_{2k}$-extended and invariant Hamiltonian $chh_k$, which can be interpreted
as a modified boson oscillator Hamiltonian. The latter is then shown to possess
a $D_{2k}$-invariant integral of motion $cyy_{2k}$, from which $Y_{2k}$ can be
obtained by projection in the $D_{2k}$ identity representation space. | | Source: | arXiv, 0911.4404 | | Services: | Forum | Review | PDF | Favorites | |
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