https://doi.org/10.1140/epjp/s13360-021-01266-6
Regular Article
Research on a new high-order generalized uncertainty principle in quantum system
1
College of Physics, Guizhou University, 550025, Guiyang, China
2
College of Mathematics, Shanghai University of Finance and Economics, 200433, Shanghai, China
3
Faculty of Physics, Shahrood University of Technology, Shahrood, Iran
Received:
9
October
2020
Accepted:
23
February
2021
Published online:
5
March
2021
Considering that curved space-time in coordinate or momentum representation should be curved, this paper proposes a new high-order generalized uncertainty principle by modifying the coordinate and momentum operator simultaneously, which could give a self-consistent phenomenological explanation for the existence of the minimum observable length. Moreover, using the proposed new high-order generalized uncertainty principle, we can deduce not only the minimum observable length, but also the allowable maximum observable momentum. More importantly, we further use the new generalized uncertainty principle to discuss the functional analysis of the position operator and maximum localization states, the compare the results with the existing literature. Finally, the harmonic oscillator is further discussed as an example.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
