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The Heun operator


por el

Dr. Alexander Turbiner

Instituto de Ciencias Nucleares, UNAM

Resumen:
It is shown that the celebrated Heun operator $(A0 x^3+ ...) \diff(2,x) + (B0 x^2+...)\diff(1,x) + C0 x$ is the $sl(2)$ quantum Euler-Arnold top of a spin $\nu$ in a constant magnetic field . For $A0 \neq 0$ it is canonically-equivalent to $A_1, BC_1$ Calogero-Moser-Sutherland quantum models, if $A0=0$, all known 1D quasi-exactly-solvable are reproduced, if in addition $B0=C0=0$ all known 1D exactly-solvable problems are reproduced. If spin $\nu$ takes (half)-integer value the Hamiltonian gets finite- dimensional invariant subspace and a number of polynomial eigenfunctions occurs.

MiƩrcoles 27 de enero, 2016
18:00 hrs.
Salón 203, Edificio Anexo, IIMAS

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