IIMAS - FENOMEC
UNAM
The Heun operator
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.
Informes: coloquiomym@gmail.com, o al 5622-3564.