Is the particle in a ring a regular Sturm-Liouville problem? The problem of a particle in a ring is a well-known eigenvalue problem $$\frac{d^2}{d\theta^2}   \psi(\theta) + V_0 \psi(\theta) = \lambda \psi(\theta)$$in physics and the Schrödinger equation has a Sturm-Liouville like form. The problem seems to be that the boundary condition $\psi(\theta + 2\pi) = \psi(\theta)$ does not seem to be very Sturm-Liouville like. Therefore, I am wondering: To which type of eigenvalue problem does this correspond?

Typical periodic Sturm-Liouville requires two conditions: $\psi(0)=\psi(2\pi)$ and $\psi'(0)=\psi'(2\pi)$.
