Kalnins, Ernie G.Miller, W., Jr.Pogosyan, G.S.2008-10-242008-10-242007-02Kalnins, E.G., Miller, W., Jr. & Pogosyan, G.S. (2007). Exact and quasiexact solvability of second order superintegrable quantum systems. II. Relation to separation of variables. Journal of Mathematical Physics, 48, 023503.0022-2488https://hdl.handle.net/10289/1150We make explicit the intimate relationship between quasiexact solvability, as expounded, for example, by Ushveridze [Quasi-exactly Solvable Models in Quantum Mechanics (IOP, Bristol, 1993)], and the technique of separation of variables as it applies to specific superintegrable quantum Hamiltonians. It is the multiseparability of superintegrable systems that forces the existence of interesting families of polynomial solutions characteristic of quasiexact solvability that enables us to solve these systems in distinct ways and that gives us the basis of a classification theory. This connection is generalized in terms of the understanding of the role of finite solutions of quantum Hamiltoniansapplication/pdfenCopyright 2007 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics and may be found at http://jmp.aip.org/jmp/top.jspMathematicsquantum theorypolynomialsJournal Article10.1063/1.2436733