SEMICLASSICAL ANALYSIS OF QUASI-EXACT SOLVABILITY

Higher-order WKB methods are used to investigate the border between th e solvable and insolvable portions of the spectrum of quasiexactly sol vable quantum-mechanical potentials. The analysis reveals scaling and factorization properties that are central to quasiexact solvability. T hese two properties define a new class of semiclassically quasiexactly solvable potentials.