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We give a brief overview of a simple and unified way, called the prepotentialapproach, to treat both exact and quasi-exact solvabilities of theone-dimensional Schr\"odinger equation. It is based on the prepotentialtogether with Bethe ansatz equations. Unlike the the supersymmetric method forthe exactly-solvable systems and the Lie-algebraic approach for thequasi-exactly solvable problems, this approach does not require any knowledgeof the underlying symmetry of the system. It treats both quasi-exact and exactsolvabilities on the same footing. In this approach the system is completelydefined by the choice of two polynomials and a set of Bethe ansatz equations.The potential, the change of variables as well as the eigenfunctions andeigenvalues are determined in the same process. We illustrate the approach byseveral paradigmatic examples of Hermitian and non-Hermitian Hamiltonians withreal energies. Hermitian systems with complex energies, called the quasinormalmodes, are also presented. Extension of the approach to the newly discoveredrationally extended models is briefly discussed.

Prepotential Approach: a unified approach to exactly, quasi-exactly, and rationally extended solvable quantal systems