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Quantum Simulation

Dirac Wave Functions of Positive Energy with Arbitrarily Small Position Uncertainty

arXiv
Authors: Ilmar Bürck, Roderich Tumulka

Year

2026

Paper ID

25798

Status

Preprint

Abstract Read

~2 min

Abstract Words

108

Citations

N/A

Abstract

We consider wave functions in the Hilbert space mathcal{H}=L2\(mathbb{R}3,mathbb{C}4\) of a single Dirac particle, specifically from the positive-energy subspace mathcal{H}_+ of the free Dirac Hamiltonian. Over the decades, various authors conjectured that for wave functions from mathcal{H}_+, there is a positive lower bound to the position uncertainty σx; in other words, that such states cannot be arbitrarily narrow in x. Building on work by Bracken and Melloy, we show that this conjecture is false. (In fact, they already stated that this conjecture is false and already had a counter-example, but their proof that it is a counter-example had a gap.)

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  • We consider wave functions in the Hilbert space mathcalH=L^2(mathbbR^3,mathbbC^4) of a single Dirac particle, specifically from the positive-energy subspace mathcalH_+ of the...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2603.04569 [2] arXiv https://arxiv.org/abs/2603.04569 [3] Publisher https://arxiv.org/abs/2603.04569

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