Exact Solutions of Schrödinger Equation with Improved Ring-Shaped Non-Spherical Harmonic Oscillator and Coulomb Potential

We propose improved ring shaped like potential of the form, V(r, θ) = V(r) + (ħ²/2Mr²)[(β sin² θ + γ cos² θ + λ) / sin θ cos θ]² and its exact solutions are presented via the Nikiforov–Uvarov method. The angle dependent part V(θ) = (ħ² / 2 Mr²)[(β sin² θ + γ cos² θ + λ) / sin θ cos θ]², which is reported for the first time embodied the novel angle dependent (NAD) potential and harmonic novel angle dependent potential (HNAD) as special cases. We discuss in detail the effects of the improved ring shaped like potential on the radial parts of the spherical harmonic and Coulomb potentials. (paper)