Exact Solutions of the Razavy Cosine Type Potential

We solve the quantum system with the symmetric Razavy cosine type potential and find that its exact solutions are given by the confluent Heun function. The eigenvalues are calculated numerically. The properties of the wave functions, which depend on the potential parameter a, are illustrated for a given potential parameter ξ. It is shown that the wave functions are shrunk to the origin when the potential parameter a increases. We note that the energy levels ϵ_i (i∈[1,3]) decrease with the increasing potential parameter a but the energy levels ϵ_i (i∈[4,7]) first increase and then decrease with the increasing a.