Radial Anharmonic Oscillator: Perturbation Theory, New Semiclassical Expansion, Approximating Eigenfunctions. I. Generalities, Cubic Anharmonicity Case

J C del Valle, A V Turbiner

For the general $D$-dimensional radial anharmonic oscillator with potential $V(r)=\frac{1}{g^2}\hat{V}(gr)$ the Perturbation Theory (PT) in powers of coupling constant $g$ (weak…