  We study an analogue of the equations describing TE and TM modes in a planar
waveguide with an arbitrary continuous dependence of the electric permittivity
and magnetic permeability on coordinates with the stationary Schr\"odinger
equation. The effective potential energies involved in the Schr\"odinger
equation for TE and TM modes are found. In general, the effective potential
energies for TE and TM modes are different but in the limit of a weak
dependence of the permittivity and permeability on coordinates they coincide.
In the case when the product of a position-dependent permittivity and
permeability is constant, it means that the refractive index is constant, we
find that the TE and TM modes are described by the supersymmtric quantum
mechanics.
