Universality in Uncertainty Relations for a Quantum Particle
| Autor: | Kechrimparis, Spiros, Weigert, Stefan |
|---|---|
| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | J. Phys. A: Math. Theor. 49 355303 (2016) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1751-8113/49/35/355303 |
| Popis: | A general theory of preparational uncertainty relations for a quantum particle in one spatial dimension is developed. We derive conditions which determine whether a given smooth function of the particle's variances and its covariance is bounded from below. Whenever a global minimum exists, an uncertainty relation has been obtained. The squeezed number states of a harmonic oscillator are found to be universal: no other pure or mixed states will saturate any such relation. Geometrically, we identify a convex uncertainty region in the space of second moments which is bounded by the inequality derived by Robertson and Schr\"{o}dinger. Our approach not only unifies existing uncertainty relations but also leads to new inequalities for second moments. Comment: 22 pages, 4 figures. Material rearranged to match published version |
| Databáze: | arXiv |
| Externí odkaz: |
|