Quantum mechanical oscillator with arbitrary anharmonicity

Properties of the 1/N expansion for the N-dimensional anharmonic oscillator with the arbitrary power anharmonicity are investigated. The first six terms of the expansion for the energy of the ground and first excited states are obtained in an analytical form. The high-order behaviour of the 1/N expansion is also studied. The formulae are derived to find the exact analytical expressions for the first six coefficients of the standard perturbation theory in powers of the coupling constant in the case of the N-dimensional double-well potential. The high-order behaviour of these coefficients is discussed