Dirac Wave Functions of Positive Energy with Arbitrarily Small Position Uncertainty
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912953909903360 |
|---|---|
| author | Bürck, Ilmar Tumulka, Roderich |
| author_facet | Bürck, Ilmar Tumulka, Roderich |
| contents | We consider wave functions in the Hilbert space $\mathcal{H}=L^2(\mathbb{R}^3,\mathbb{C}^4)$ 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 $σ_x$; 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.) |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04569 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dirac Wave Functions of Positive Energy with Arbitrarily Small Position Uncertainty Bürck, Ilmar Tumulka, Roderich Quantum Physics We consider wave functions in the Hilbert space $\mathcal{H}=L^2(\mathbb{R}^3,\mathbb{C}^4)$ 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 $σ_x$; 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.) |
| title | Dirac Wave Functions of Positive Energy with Arbitrarily Small Position Uncertainty |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.04569 |