Exact Heisenberg operator solutions for multi-particle quantum mechanics

Details Exact Heisenberg operator solutions for multi-particle quantum mechanics Exact Heisenberg operator solutions for multi-particle quantum mechanics

2007-06-06

arxiv.org/abs/0706.0768v1

J. Math. Phys. 48 (2007) 082106 (12pp)

Physics

Quantum Physics

17 pages, no figures

Scientific paper

10.1063/1.2771544

Exact Heisenberg operator solutions for independent `sinusoidal coordinates' as many as the degree of freedom are derived for typical exactly solvable multi-particle quantum mechanical systems, the Calogero systems based on any root system. These Heisenberg operator solutions also present the explicit forms of the annihilation-creation operators for various quanta in the interacting multi-particle systems. At the same time they can be interpreted as multi-variable generalisation of the three term recursion relations for multi-variable orthogonal polynomials constituting the eigenfunctions.

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