Issue |
EPL
Volume 89, Number 5, March 2010
|
|
---|---|---|
Article Number | 50008 | |
Number of page(s) | 5 | |
Section | General | |
DOI | https://doi.org/10.1209/0295-5075/89/50008 | |
Published online | 25 March 2010 |
On the modification of the Hamiltonians' spectrum in gravitational quantum mechanics
Plasma Physics Research Center, Science and Research Campus, Islamic Azad University - Tehran, Iran
Corresponding author: pouria.pedram@gmail.com
Received:
20
January
2010
Accepted:
22
February
2010
Different candidates of quantum gravity such as string theory, doubly special relativity, loop quantum gravity and black-hole physics all predict the existence of a minimum observable length or a maximum observable momentum which modifies the Heisenberg uncertainty principle. This modified version is usually called the generalized (gravitational) uncertainty principle (GUP) and changes all Hamiltonians in quantum mechanics. In this letter, we use a recently proposed GUP which is consistent with string theory, doubly special relativity and black-hole physics and predicts both a minimum measurable length and a maximum measurable momentum. This form of GUP results in two additional terms in any quantum-mechanical Hamiltonian, proportional to α and α2, respectively, where α ~ 1/MPlc is the GUP parameter. By considering both terms as perturbations, we study two quantum-mechanical systems in the framework of the proposed GUP: a particle in a box and a simple harmonic oscillator. We demonstrate that, for the general polynomial potentials, the corrections to the highly excited eigenenergies are proportional to their square values. We show that this result is exact for the case of a particle in a box.
PACS: 04.60.-m – Quantum gravity
© EPLA, 2010
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.