Exchange operator formalism for an infinite family of solvable and integrable quantum systems on a plane - Mathematical PhysicsReport as inadecuate




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Abstract: The exchange operator formalism in polar coordinates, previously consideredfor the Calogero-Marchioro-Wolfes problem, is generalized to a recentlyintroduced, infinite family of exactly solvable and integrable Hamiltonians$H k$, $k=1$, 2, 3,

., on a plane. The elements of the dihedral group $D {2k}$are realized as operators on this plane and used to define somedifferential-difference operators $D r$ and $D {\varphi}$. The latter serve toconstruct $D {2k}$-extended and invariant Hamiltonians $\chh k$, from which thestarting Hamiltonians $H k$ can be retrieved by projection in the $D {2k}$identity representation space.



Author: C. Quesne

Source: https://arxiv.org/



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