ANHARMONIC-OSCILLATOR AND ITS DEPENDENCE ON SPACE DIMENSIONS

The perturbation series (PS) in powers of g for the D-dimensional gr4 anharmonic oscillator is considered. High-order terms of the ground-state-energy E(g, D) expansion are explicitly calculated with the help of recurrence relations among integers. The rate of approach of the PS coefficients to the asymptotic value as a function of D is investigated. For the case of D = 0 explicit solutions are obtained and analytic properties of E(g, 0) are briefly discussed. For D ≫ 1 the first terms in the expansion of E(g, D) in powers of D-1 are found. © 1979.