Given the Hamiltonian $$ H=p^{2}-ge^{-x}, $$ are the energies negative?
If I impose the boundary condition $y(0)=0$ and $y(\infty)=0$, I get the condition for the energies $$ J_{2i \sqrt{E(n)}}(g) =0 $$ where $J_{a}(x)$ is a Bessel function.
Unfortunately, this is too hard to solve, so how can I obtain the quantization of the energy levels in the WKB approximation?
