Quasi-Exactly Solvable Models in Quantum Mechanics

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 modern quantum physics. Quasi-exactly solvable (QES) models (whose Hamiltonians admit an explicit diagonalization only for some limited segments of the spectrum) provide a practical way forward.

Although QES models are a recent discovery, the results are already numerous. Collecting the results of QES models in a unif...