Nonlinear Schrödinger equations and generalized Heisenberg uncertainty principle from estimation schemes violating the principle of estimation independence

The Improvement of the Heisenberg Uncertainty Principle

On Generalized Uncertainty Principle

We study generalized uncertainty principle through the basic concepts of limit and Fourier transformation to analyze the quantum theory of gravity or string theory from the perspective of a complex function. Motivated from the noncommutative nature of string theory, we have proposed a UV/IR mixing dependent function δ̃(∆x,∆k, ǫ). We arrived at the string uncertainty principle from the analyticit...

Generalized Uncertainty Principle and Quantum

In the present work the role that a generalized uncertainty principle could play in the quantization of the electromagnetic field is analyzed. It will be shown that we may speak of a Fock space, a result that implies that the concept of photon is properly defined. Nevertheless, in this new context the creation and annihilation operators become a function of the new term that modifies the Heisen...

An Infinite - Dimensional Heisenberg Uncertainty Principle

An analogue of the classical Heisenberg inequality is given for an infinite-dimensional space. The proof relies on a commutation relationship and integration by parts formula for Gaussian measure. We also discuss when the equality holds.

Quantum Mechanics and the Generalized Uncertainty Principle

There is reason to believe in the existence of a minimal length that can in principle be measured. This viewpoint stems in part from the realization that if enough massenergy is confined to a small region of space, a black hole must form. For example if one increases the energy of colliding particles beyond the Planck energy, one expects the short distance effects to be hidden behind an event h...