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When electrodynamics is quantized in a situation where the electrons existonly at a flat surface such as graphene, one of the Maxwell equations appearsas a local part of the Hamiltonian. As a consequence of gauge invariance, anyphysical state has to be a zero-energy state of the local Hamiltonian. Weconstruct two stationary quantum states; one reproduces scattering andabsorption of light, which is familiar in classical optics and the other ismore fundamentally related to photon creation. These two states are inseparableby the Hamiltonian and forming a two-state system, but there is a specialnumber of surfaces for which two states are decoupled. The number is $2/\pi\alpha$ where $\pi \alpha$ is the absorption probability of single surface.

Stationary Two-State System in Optics using Layered Materials