  We consider two models where the wave equation can be reduced to the
effective Schr\"odinger equation whose potential contains both harmonic and the
Coulomb terms, $\omega^{2}r^{2}-a/r$. The equation reduces to the biconfluent
Heun's equation, and we find that the charge as well as the energy must be
quantized and state dependent. We also find that two quantum numbers are
necessary to count radial degrees of freedom and suggest that this is a general
feature of differential equation with higher singularity like the Heun's
equation.
