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We analyze the behavior of a non-Hermitian opened one-dimensional quantumsystem with Parity-Time ($\mathcal{PT}$) symmetry. This system is built by adimer, which has balanced gains and losses described by a parameter $\gamma$.By varying $\gamma$ the system resonances, which are naturally separated,coalesce at the exceptional point (EP). The transmission spectrum is obteinedby means of the scattering matrix ($S$ matrix) formalism and we examine thewave functions corresponding to the resonances as a function of $\gamma$.Specifically, we look for the behavior and distribution of the phases of the Smatrix before, at and after the exceptional point.

Exceptional Points in a $\mathcal{PT}$-symmetrical quantum system: a Scattering matrix approach