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We propose a new SUSY method for construction of the quasi-exactly solvable(QES) potentials with three known eigenstates. New QES potentials andcorresponding energy levels and wave functions of the ground state and twolowest excited state are obtained. The proposed scheme allows also to constructfamilies of exactly solvable non-singular potentials which are SUSY partners ofthe well-known ones.Comment: 15 pages, LaTeX, no figures, revised versio

Quasi-exactly solvable potentials with three known eigenstates