Eigenvalues of the differential operator $-\frac{d^2}{dx^2} + k\left( \frac{x}{a} - \frac{a}{x}\right)^2$ on $(0,\infty)$.

Question

I'm trying to solve for the eigenvalues of the differential operator $$-\frac{d^2}{dx^2} + k\left( \frac{x}{a} - \frac{a}{x}\right)^2$$ over square-integrable functions on $(0,\infty)$ where $k,a$ are positive real constants. In other words, is there a simple solution to the differential equation $$-\frac{d^2y}{dx^2} + k\left( \frac{x}{a} - \frac{a}{x}\right)^2 y = \lambda y$$ with $y(0)=0$ and $\lim_{x \to \infty} y(x) = 0$, and if not, is there a way to determine the set of eigenvalues $\{\lambda\}$ ?