[BOOK][B] Quasi-exactly solvable models in quantum mechanics

AG Ushveridze - 2017 - taylorfrancis.com
Exactly solvable models, that is, models with explicitly and completely diagonalizable
Hamiltonians are too few in number and insufficiently diverse to meet the requirements of …

[PDF][PDF] Quasi-exact solvability

A Gonzalez-Lopez, N Kamran… - Contemporary …, 1994 - researchgate.net
ARTEMIo GoNzÁLEz-LóEz, NIKY KAMRAN, AND PETER J. OLVER Page 1 eAAA
Contemporary Mathetnatics Volunne 1 60, 1994 QUASI-EXACT SOLVABILITY ARTEMIo …

Exact solvability of superintegrable systems

P Tempesta, AV Turbiner, P Winternitz - arxiv preprint hep-th/0011209, 2000 - arxiv.org
It is shown that all four superintegrable quantum systems on the Euclidean plane possess
the same underlying hidden algebra $ sl (3) $. The gauge-rotated Hamiltonians, as well as …

Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators

A Gonzalez-Lopez, N Kamran, PJ Olver - … in Mathematical Physics, 1993 - Springer
We completely determine necessary and sufficient conditions for the normalizability of the
wave functions giving the algebraic part of the spectrum of a quasi-exactly solvable …

LIE-ALGEBRAS AND LINEAR OPERATORS WITH INVARIANT

A Turbiner - Lie Algebras, Cohomology, and New Applications to …, 1994 - books.google.com
A general classification of linear differential and finite-difference operators possessing a
finite-dimensional invariant subspace with a polynomial basis (the generalized Bochner …

Criterion for polynomial solutions to a class of linear differential equations of second order

N Saad, RL Hall, H Ciftci - Journal of Physics A: Mathematical …, 2006 - iopscience.iop.org
We consider the differential equations y''= λ 0 (x) y'+ s 0 (x) y, where λ 0 (x), s 0 (x) are C∞-
functions. We prove (i) if the differential equation has a polynomial solution of degree n> 0 …

Tridiagonalization and the Heun equation

FA Grünbaum, L Vinet, A Zhedanov - Journal of Mathematical Physics, 2017 - pubs.aip.org
It is shown that the tridiagonalization of the hypergeometric operator L yields the generic
Heun operator M. The algebra generated by the operators L, M and Z=[L, M] is quadratic and …

Algebraization of difference eigenvalue equations related to Uq (sl2)

PB Wiegmann, AX Zabrodin - Nuclear Physics B, 1995 - Elsevier
A class of second order difference (discrete) operators with a partial algebraization of the
spectrum is introduced. The eigenfuncions of the algebraized part of the spectrum are …

Two electrons in an external oscillator potential: The hidden algebraic structure

A Turbiner - Physical Review A, 1994 - APS
It is shown that the Coulomb correlation problem for a system of two electrons (two charged
particles) in an external oscillator potential possesses a hidden sl 2-algebraic structure …

Lie algebraic discretization of differential equations

Y Smirnov, A Turbiner - Modern Physics Letters A, 1995 - World Scientific
A certain representation for the Heisenberg algebra in finite difference operators is
established. The Lie algebraic procedure of discretization of differential equations with …