Uncertainty relations in curved spaces

Abstract

Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in details. The investigation can be of interest for string and brane theory, solid state physics (quantum wires) and quantum optics.

published version; phase space structure discussion added

References in corpus (1)

• Self-adjoint extensions of operators and the teaching of quantum mechanics

Cited by in corpus (7)

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• Schwinger Pair Production and the Extended Uncertainty Principle: Can Heuristic Derivations Be Trusted?
• On the uncertainty principle in Rindler and Friedmann spacetimes
• Thin layer quantization in higher dimensions and codimensions
• On momentum operators given by Killing vectors whose integral curves are geodesics
• Position Uncertainty Measures on the Sphere
• Non-Hermiticities even in quantum systems that are closed