Minimum-Uncertainty Angular Wave Packets and Quantized Mean Values

Physics – Quantum Physics

Scientific paper

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accepted for publication in Physical Review A

Scientific paper

10.1103/PhysRevA.53.1978

Uncertainty relations between a bounded coordinate operator and a conjugate momentum operator frequently appear in quantum mechanics. We prove that physically reasonable minimum-uncertainty solutions to such relations have quantized expectation values of the conjugate momentum. This implies, for example, that the mean angular momentum is quantized for any minimum-uncertainty state obtained from any uncertainty relation involving the angular-momentum operator and a conjugate coordinate. Experiments specifically seeking to create minimum-uncertainty states localized in angular coordinates therefore must produce packets with integer angular momentum.

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