Conservation laws for a $q$-deformed nonrelativistic particle

We derive $q$-versions of Green's theorem from the Leibniz rules of partial derivatives for the $q$-deformed Euclidean space. Using these results and the Schrödinger equations for a $q$-deformed nonrelativistic particle, we derive continuity equations for the probability density, the energy density, and the momentum density of a $q$-deformed nonrelativistic particle.

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