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In quantum scattering theory, the time evolution of a physical system can be described as a series of unitary transformations. The operator of this transformation will be denotedS   ̂$\hat{\boldsymbol{S}}$; the corresponding matrix is the  Ŝ -matrix (scattering matrix). This last object contains all the information on the broadcast process associated with the operatorS   ̂$\hat{\boldsymbol{S}}$The present work has two objectives: To develop the one-dimensional formalism of the scattering matrix of relativistic particles of spin-s ( s  = 0, 1/2) in the presence of a localized electromagnetic field on the one hand and on the other hand to analyze the solutions of the problem of scattering states of relativistic particles of spin-s in interaction with some localized scalar potentials via theŜ$\hat{S}$-matrix formalism.

Relativistic Ŝ -matrix formulation in one dimension for particles of spin-s ( s = 0, 1/2)