QUANTIZATION RULES FOR BOUND-STATES IN QUANTUM-WELLS

An algebraic reformulation of the Bohr-Sommerfeld (BS) quantization ru le is suggested and applied to the study of bound states in one-dimens ional quantum wells. The energies obtained with the present quantizati on rule are compared to those obtained with the usual BS and WKB quant ization rules and with the exact solution of the Schrodinger equation. We find that, in diverse cases of physical interest in molecular phys ics, the present quantization rule not only yields a good approximatio n to the exact solution of the Schrodinger equation, but yields more p recise energies than those obtained with the usual BS and/or WKB quant ization rules. Among the examples considered numerically are the Poesc hl-Teller potential and several anharmonic oscillator potentials. whic h simulate molecular vibrational spectra and the problem of an isolate d quantum well structure subject to an external electric field.