Radial anharmonic oscillator: Perturbation theory, new semiclassical expansion, approximating eigenfunctions. II. Quartic and sextic anharmonicity cases

In our previous paper I (del Valle-Turbiner, 2019) a formalism was developed to study the general D-dimensional radial anharmonic oscillator with potential V(r) = 1/g(2) (V) over cap (gr). It was based on the Perturbation Theory (PT) in powers of g (weak coupling regime) and in inverse, fractional powers of g (strong coupling regime) in both r-space and in (gr)-space, respectively. As a result, the Approximant was introduced - a locallyaccurate uniform compact approximation of a wave function. If taken as a trial function in variational calculations, it has led to variational energies of unprecedented accuracy for cubic anharmonic oscillator. In this paper, the formalism is applied to both quartic and sextic, spherically-symmetric radial anharmonic oscillators with two term potentials V(r) = r(2) + g(2(m -1))r(2m), m = 2, 3, respectively. It is shown that a two-parametric Approximant for quartic oscillator and a five-parametric one for sextic oscillator for the first four eigenstates used to calculate the variational energy are accurate in 8-12 figures for any D = 1, 2, 3, ... and g >= 0, while the relative deviation of the Approximant from the exact eigenfunction is less than 10(-6) for any r >= 0.