Nonrelativistic one-particle problem on q-deformed Euclidean space
Abstract
We consider time-dependent Schr\"odinger equations for a free nonrelativistic particle on the three-dimensional q-deformed Euclidean space. We determine plane wave solutions to these Schr\"odinger 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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