HIGHER-ORDER HARMONIC OSCILLATOR PERTURBED BY ALMOST PERIODIC POTENTIAL

We study the perturbation L = H+V in L 2 (R), where H = (-1) l d 2l dx 2l + x 2l , l N * , and V is an almost periodic potential with uniformly continuous derivatives V (n) .We assume that the eigenvalues of L around k can be written in the form k + k .We establish an asymptotic formula for the fluctuations { k }, which are determined by a transformation of V .