The woks of, one important observation was that various observableĮffects of the minimal length uncertainty relation are non-perturbative in theĭeformation parameter β, ( i.e., contain all orders In this direction, some remarks can be made about Eqs. So a new (high energy) uncertainty principle was obtained. Note here that Saavedra and Utreras were the first to propose a generalization of the canonicalĬommutation relations of quantum mechanics which should be important at highĮnergies. Usually termed the generalized uncertainty principle (GUP) or the minimal length This modification of the uncertainty relation is Which clearly implies the existence of a non-zero minimal △ x min = ℏ β ∼ l p where l p is the Planck length. Relation between position and momentum operators becomes Uncertainty in position measurement, so that the usual canonical commutation This minimal length can be introduced as an additional String scale ℏ β, where β is a small positive parameter called theĭeformation parameter. Uncertainty relation has appeared in the context of the string theory, where it is aĬonsequence of the fact that the string cannot probe distances smaller than the Heisenberg uncertainty principle should be reformulated. AllĪpproaches of quantum gravity show the idea that near the Planck scale, the standard
The existence of a minimal measurable length on the order of the Planck length. One of the most important problems in theoretical physics. The unification between the general theory of relativity and the quantum mechanics is Reproduced with high accuracy those derived using the Rung-Kutta method. The results obtained using the Dirac oscillator basis The Dirac-oscillator basis and are then compared against results obtained with the Ground-state densities for a selected set of doubly-magic magic are performed using Self-consistent calculations of binding energies and Systems without spherical symmetry as required in constrained calculations of Piekarewicz illustrate the power andįlexibility of the Dirac oscillator and they suggest extensions to the study of The experimental results obtained,Ĭoncerning the spectrum of the one-dimensional DO with and without the mass term,Īre in good agreement with those obtained in the theory. The experiment relies on a relation of the DO exposed the proposal of the first experimental microwave Physical applications (see and references Oscillator has attracted a lot of interest both because it provides one of theĮxamples of the Dirac’s equation exact solvability and because of its numerous TheĮlectromagnetic potential associated with the DO has been found by Benitez The interaction of the anomalous magnetic moment with a linear electric field. That the DO interaction represents a physical system, which can be interpreted as They considered a Dirac equation in which the momentum p → is replaced by p → - i m β ω r →, with r → being the position vector, m the mass of particle, and Potential both the theoretical and application implications. The Dirac relativistic oscillator is an important Non-relativistic limit, it becomes a harmonic oscillator with a very strong Oscillator was revived by Moshinsky and Szczepaniak, who gave it the name of Dirac oscillator (DO) because, in the The wellknown relativistic model of the harmonic The studies of the relativistic generalization of the harmonic oscillator has drawn
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