Sextic anharmonic oscillators and Heun differential equations

With certain constraints on the parameters μ _4 and μ _2 , it is known that the Schrödinger equation with the sextic anharmonic oscillator potential V(r)=r^6+μ _4 r^4+μ _2 r^2 is quasi-exactly solvable. Here, we solve the Schrödinger equation for arbitrary values of the potential parameters in the d -dimensional case. The method discussed offers a practical solution to the biconfluent Heun equation’s eigenvalue problem. A technique based on the asymptotic iteration method is used to evaluate the coefficients of the series solutions for arbitrary μ _4 and μ _2 .