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

Abstract

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.

34 pages, 5 Postscript figures, title has been changed, some typographical errors have been corrected, some passages in the text have been revised for better comprehensibility

References in corpus (4)

• Gauge Theory on Noncommutative Spaces
• q-Integration on Quantum Spaces
• Analysis on q-deformed quantum spaces
• Quantum Dynamics on the three-dimensional q-deformed Euclidean Space