The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field
By Pouria Pedram, Kourosh Nozari, S. Taheri. 2011
135 citations recorded by the source corpus.
The existence of a minimum observable length and/or a maximum observable momentum is in agreement with various candidates of quantum gravity such as string theory, loop quantum gravity, doubly special relativity and black hole physics. In this scenario, the Heisenberg uncertainty principle is changed to the so-called Generalized (Gravitational) Uncertainty Principle (GUP) which results in modification of all Hamiltonians in quantum mechanics. In this paper, following a recently proposed GUP which is consistent with quantum gravity theories, we study the quantum mechanical systems in the presence of both a minimum length and a maximum momentum. The generalized Hamiltonian contains two additional terms which are proportional to αp3 and α2p4 where α ∼ 1/MPlc is the GUP parameter. For the case of a quantum bouncer, we solve the generalized Schrödinger equation in the momentum space and find the modified energy eigenvalues and eigenfunctions up to the second-order in GUP parameter. The effects of the GUP on the transition rate of ultra cold neutrons in gravitational spectrometers are discussed finally.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/b2005dfdd3c2618d269f1c544cfa072a36102372
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In Atomic and Molecular Physics, and Optics
In Statistical and Nonlinear Physics
Citations in the corpus
- Minimal Length Scale Scenarios for Quantum Gravity (2012, unknown): “calculated the quantization of the energy spectrum of a particle in a linear gravitational field in the GUP leading-order approximation [259] and to all orders [256].”
- Generalized Uncertainty Principle: Approaches and Applications (2014, background): “• scattering problem in deformed space with minimal length [86], • ultra-cold neutrons in gravitational field with minimal length [87–89], • influence of minimal length on Lamb shift, Landau levels, and tunnelling current in scanning tunnelling microscope [75, 90]”