The uncertainty principles of the 1-D fractional Fourier transform and the 1-D linear canonical transform have been derived. We extend the previous works and discuss the uncertainty principle for the two-dimensional affine generalized Fourier transform (2-D AGFFT). We find that derived uncertainty principle of the 2-D AGFFT can also be used for determining the uncertainty principles of many 2-D...

here, we have considered the husimi and wigner distribution functions. we have, inparticular, shown how the uncertainty principle works for the two cases of simple and damped harmonicoscillators when either of these two distributions are used. the conclusion shows that the husimidistribution function remains non-negative through the phase space but it does not always satisfies theuncertainty pr...

We construct a quantum theory of free scalar field in 1+1 dimensions based on the deformed Heisenberg algebra [x̂, p̂] = i~(1 + βp̂) where β is a deformation parameter. Both canonical and path integral formalism are employed. A higher dimensional extension is easily performed in the path integral formalism. [email protected] [email protected]

In this letter, we investigate a possible modification to the temperature and entropy of 5−dimensional Schwarzschild anti de Sitter black holes due to incorporating stringy corrections to the modified uncertainty principle. Then we subsequently argue for corrections to the Cardy-Verlinde formula in order to account for the corrected entropy. Then we show, one can taking into account the general...

Extensions (modi cations) of the Heisenberg Uncertainty principle are derived within the framework of the theory of Special Scale-Relativity proposed by Nottale. In particular, generalizations of the Stringy Uncertainty Principle are obtained where the size of the strings is bounded by the Planck scale and the size of the Universe. Based on the fractal structures inherent with two dimensional Q...

The minisuperspace dynamics of the Friedmann-Robertson-Walker (FRW) and of the Taub Universes in the context of a Generalized Uncertainty Principle is analyzed in detail. In particular, the motion of the wave packets is investigated and, in both the models, the classical singularity appear to be probabilistic suppressed. Moreover, the FRW wave packets approach the Planckian region in a stationa...