English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The existence of a minimum observable length and/or a maximum observablemomentum is in agreement with various candidates of quantum gravity such asstring theory, loop quantum gravity, doubly special relativity and black holephysics. In this scenario, the Heisenberg uncertainty principle is changed tothe so-called Generalized (Gravitational) Uncertainty Principle (GUP) whichresults in modification of all Hamiltonians in quantum mechanics. In thispaper, following a recently proposed GUP which is consistent with quantumgravity theories, we study the quantum mechanical systems in the presence ofboth a minimum length and a maximum momentum. The generalized Hamiltoniancontains two additional terms which are proportional to $\alpha p^3$ and$\alpha^2 p^4$ where $\alpha \sim 1/M_{Pl}c$ is the GUP parameter. For the caseof a quantum bouncer, we solve the generalized Schrodinger equation in themomentum space and find the modified energy eigenvalues and eigenfunctions upto the second-order in GUP parameter. The effects of the GUP on the transitionrate of ultra cold neutrons in gravitational spectrometers are discussedfinally.

The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field