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This study presents an alternating coordinate-momentum representation for propagation and transition of associated wave function, based on Bopp operators and on a certain symbolic determinant corresponding to a set of two linear equations with null free terms. It is shown that this alternating representation can justify in a good manner the patterns created through reflection/refraction of waves on nonperfectly smooth interfaces and phase correspondence of diffracted beams without the need ofdoi:10.1155/2015/818019 fatcat:aew2rgm3czhlbdzeyiumngyrhe