52 research outputs found
A class of GUP solutions in deformed quantum mechanics
Various candidates of quantum gravity such as string theory, loop quantum
gravity and black hole physics all predict the existence of a minimum
observable length which modifies the Heisenberg uncertainty principle to
so-called Generalized Uncertainty Principle (GUP). This approach results in the
modification of the commutation relations and changes all Hamiltonians in
quantum mechanics. In this paper, we present a class of physically acceptable
solutions for a general commutation relation without directly solving the
corresponding generalized Schrodinger equations. These solutions satisfy the
boundary conditions and exhibit the effect of the deformed algebra on the
energy spectrum. We show that, this procedure prevents us from doing equivalent
but lengthy calculations.Comment: 9 pages, 1 figur
A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum II: Applications
In a recent paper, we presented a nonperturbative higher order generalized
uncertainty principle (GUP) that is consistent with various proposals of
quantum gravity such as string theory, loop quantum gravity, doubly special
relativity, and predicts both a minimal length uncertainty and a maximal
observable momentum. In this Letter, we find exact maximally localized states
and present a formally self-adjoint and naturally perturbative representation
of this modified algebra. Then we extend this GUP to D dimensions that will be
shown it is noncommutative and find invariant density of states. We show that
the presence of the maximal momentum results in upper bounds on the energy
spectrum of the free particle and the particle in box. Moreover, this form of
GUP modifies blackbody radiation spectrum at high frequencies and predicts a
finite cosmological constant. Although it does not solve the cosmological
constant problem, it gives a better estimation with respect to the presence of
just the minimal length.Comment: 15 pages, 3 figures, second part of arXiv:1110.2999, to appear in
Physics Letters
On the boundary conditions in deformed quantum mechanics with minimal length uncertainty
We find the coordinate space wave functions, maximal localization states, and
quasiposition wave functions in a GUP framework that implies a minimal length
uncertainty using a formally self-adjoint representation. We show that how the
boundary conditions in quasiposition space can be exactly determined from the
boundary conditions in coordinate space.Comment: 9 pages, to appear in Advances in High Energy Physic
Exact Ultra Cold Neutrons' Energy Spectrum in Gravitational Quantum Mechanics
We find exact energy eigenvalues and eigenfunctions of the quantum bouncer in
the presence of the minimal length uncertainty and the maximal momentum. This
form of Generalized (Gravitational) Uncertainty Principle (GUP) agrees with
various theories of quantum gravity and predicts a minimal length uncertainty
proportional to and a maximal momentum proportional to
, where is the deformation parameter. We also find the
semiclassical energy spectrum and discuss the effects of this GUP on the
transition rate of the ultra cold neutrons in gravitational spectrometers.
Then, based on the Nesvizhevsky's famous experiment, we obtain an upper bound
on the dimensionless GUP parameter.Comment: 11 pages, 1 figure, to appear in European Physical Journal
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