Abstract
The lack of experimental results of theories concerning the ultimate space/space–time structure, leads one to think about some simple experiments that can help demonstrate the main prediction: Space–time is discrete. In this paper, an implementation of Snyder operators is applied to simple geometries, to demonstrate that the spectrum of the position operator, in standard quantum mechanics (QM), is discrete when a parameter measuring the non-commutativity of quantum operators is introduced. The geometries are specially suitable for experiments in search of the behaviour of ultracold neutrons falling in the Earth’s gravitational potential.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J Magueijo and L Smolin, Phys. Rev. Lett. 88, 190403 (2002), https://doi.org/10.1103/PhysRevLett.88.190403 [hep-th/0112090]
J Magueijo and L Smolin, Class. Quant. Grav. 21, 1725 (2004), https://doi.org/10.1088/0264-9381/21/7/001 [gr-qc/0305055]
H Snyder, Phys. Rev. 71, 38 (1947)
J M Romero and J D Vergara, Mod. Phys. Lett. A 18, 1673 (2003), [hep-th/0303064]
C Leiva, J Saavedra and J R Villanueva, Pramana – J. Phys. 80, 945 (2013), https://doi.org/10.1007/s12043-013-0540-5 [arXiv:1211.6785 [gr-qc]]
S Mignemi and R Strajn, Phys. Rev. D 90(4), 044019 (2014), https://doi.org/10.1103/PhysRevD.90.044019 [arXiv:1404.6396 [gr-qc]]
S A Franchino-Vias and S Mignemi, Phys. Rev. D 98(6), 065010 (2018), https://doi.org/10.1103/PhysRevD.98.065010[arXiv:1806.11467 [hep-th]]
S Meljanac, D Meljanac, S Mignemi and R Strajn, Phys. Lett. B 768, 321 (2017), https://doi.org/10.1016/j.physletb.2017.02.059[arXiv:1701.05862 [hep-th]]
C Leiva, J. Phys. Conf. Ser. 33, 417 (2006), https://doi.org/10.1088/1742-6596/33/1/052
M V Battisti and S Meljanac, Phys. Rev. D 82, 024028 (2010), https://doi.org/10.1103/PhysRevD.82.024028[arXiv:1003.2108 [hep-th]]
M Maggiore, Phys. Lett. B 304, 65 (1993), https://doi.org/10.1016/0370-2693(93)91401-8 [hep-th/ 9301067]
S Mignemi, Class. Quant. Grav. 29, 215019 (2012), https://doi.org/10.1088/0264-9381/29/21/215019 [arXiv:1110.0201 [hep-th]]
H Calisto and C Leiva, Int. J. Mod. Phys. D 16, 927 (2007), https://doi.org/10.1142/S021827180701050X [hep-th/0509227]
P Pedram, Eur. Phys. J. C 73, 2609 (2013), https://doi.org/10.1140/epjc/s10052-013-2609-1 [arXiv:1309.7284 [hep-th]]
H Abele, T Jenke, D Stadler and P Geltenbort, Nucl. Phys. A 827, 593c (2009), https://doi.org/10.1016/j.nuclphysa.2009.05.131
M Utsuro, J. Phys. Colloq. 45(C3), 269 (1984), https://doi.org/10.1051/jphyscol:1984345
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Leiva, C., Romero, S. Realisation of Snyder operators in quantum mechanics. Pramana - J Phys 95, 58 (2021). https://doi.org/10.1007/s12043-021-02099-9
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12043-021-02099-9