# Exchange operator formalism for an infinite family of solvable and integrable quantum systems on a plane - Mathematical Physics

Exchange operator formalism for an infinite family of solvable and integrable quantum systems on a plane - Mathematical Physics - Download this document for free, or read online. Document in PDF available to download.

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/