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Abstract: Exact Heisenberg operator solutions for independent `sinusoidal coordinates-as many as the degree of freedom are derived for typical exactly solvablemulti-particle quantum mechanical systems, the Calogero systems based on anyroot system. These Heisenberg operator solutions also present the explicitforms of the annihilation-creation operators for various quanta in theinteracting multi-particle systems. At the same time they can be interpreted asmulti-variable generalisation of the three term recursion relations formulti-variable orthogonal polynomials constituting the eigenfunctions.



Author: Satoru Odake, Ryu Sasaki

Source: https://arxiv.org/



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