[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 …
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 …
Contemporary Mathetnatics Volunne 1 60, 1994 QUASI-EXACT SOLVABILITY ARTEMIo …
Exact solvability of superintegrable systems
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 …
the same underlying hidden algebra $ sl (3) $. The gauge-rotated Hamiltonians, as well as …
Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators
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 …
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 …
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
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 …
functions. We prove (i) if the differential equation has a polynomial solution of degree n> 0 …
Tridiagonalization and the Heun equation
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 …
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)
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 …
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 …
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 …
established. The Lie algebraic procedure of discretization of differential equations with …