Nonrelativistic one-particle problem on $q$-deformed Euclidean space

We consider time-dependent Schrödinger equations for a free nonrelativistic particle on the three-dimensional $q$-deformed Euclidean space. We determine plane wave solutions to these Schrödinger equations and show that they form a complete orthonormal system. We derive $q$-deformed expressions for propagators of a nonrelativistic particle. Considerations about expectation values for position or momentum of a nonrelativistic particle conclude our studies.

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