Representation of Solutions of Radial Schrodinger Equation for The Double An-Harmonic Oscillator via Transformation to Biconfluent Heunsequation

Abstract

In this work, we study the Radia Schrondinger equation corresponding to a double an-harmonic oscillator potential. By means of an appropriate change of variables and a suitable transformation of the wave function, the radial equation is reduced to the canonical form of the biconfluent Heun equation. This transformation enables the representation of exact and quasi-exact solutions in terms of biconfluent Heun functions. We derive the conditions under which polynomial solutions arise, leading to discrete energy spectral and physically acceptable bound states. The obtained results provide a unified analytical framework for treating double an-harmonic oscillator potentials and highlight the relevance of Heun type equations in quantum mechanical systems with non-polynomial potentials. The solution of Radial Schrodinger equation for the double An Harmonic Oscillator via transformation of the Schrodinger equation to Biconfluent Heun’s equation. The representation of this solution is explicitly expressed. Our approach offers deeper insight into the spectral properties of the model and facilities further analytical and numerical investigations