Chair for Theoretical Physics,

Ivan Franko National University of Lviv,

12 Drahomanov Str., Lviv, UA-79005, UKRAINE

E-mail: tkachuk@ktf.franko.lviv.ua

**Supersymmetric approach for generating quasi-exactly
solvable potentials**

**Abstract:**

Recently much attention has been given to the quasi-exactly solvable
(QES) potentials, for which a finite number of energy levels and corresponding
wave functions are known in an explicit form. In the frame of supersymmetric
(SUSY)quantum mechanics we propose the inverse method for constructing
the QES potentials with arbitrary two known energy levels and corresponding
wave functions. The QES potential and the wave functions of the two energy
levels are expressed by some generating function the properties of which
determine the state numbers of these levels. Choosing different generating
functions we present the explicit examples of the QES potentials. Multidimensional
QES potentials are also discussed.