Semi-exact solutions of sextic potential plus a centrifugal term

Abstract

We revisit the one-dimensional quantum system of a sextic potential added with a centrifugal term, V(x)=ax(-2)+bx(2)+cx(4)+dx(6), where the parameters a,b,c and d are arbitrary. We find that its solutions can be expressed as a Biconfluent Heun function H-B(alpha,beta,gamma,delta z), while the associated energy spectrum is determined by the parameter delta. The semi-exact solutions of wave functions fully consist with the properties of the potential.