On the basis of generalized classical kinetic equations, reproducing the stationary distribution of the Tsallis nonextensive thermostatistics, we formulate two generalized Schr¨odinger equations which satisfy the basic assumptions of the quantum mechanics under an appropriate generalization of the operator properties. Moreover, we study the generalization of the previously introduced dynamic equations in a relativistic regime and we apply our results to the study of the rapidity distribution in the relativistic heavy-ion collisions.
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