Minimum-Uncertainty Angular Wave Packets and Quantized Mean Values
arXiv:quant-ph/9512030 · doi:10.1103/PhysRevA.53.1978
Abstract
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.
accepted for publication in Physical Review A
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