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Uncertainty Relations (uncertainty + relation)

Distribution by Scientific Domains
Physics and Astronomy40%

Selected Abstracts

A new look at the derivation of the Schrödinger equation from Newtonian mechanics

ANNALEN DER PHYSIK, Issue 6 2003
L. Fritsche
Abstract We present a modified version of Nelson's seminal paper on the derivation of the time-dependent Schrödinger equation which draws on the equation of motion of a particle that moves under the influence of a classical force field and additional stochastic forces. The emphasis of our elaboration is focused on the implication of allowing stochastic forces to occur, viz. that the energy E of the particle is no longer conserved on its trajectory in a conservative force field. We correlate this departure , E from its classical energy with the energy/time uncertainty relation where , t is the average time for , E to persist. The stability of atoms, the zero-point energy of oscillators, the tunneling effect and the diffraction at slits are shown to be directly connected with the occurrence of such energy fluctuations. We discuss and rederive Nelson's theory entirely from this point of view and generalize his approach to systems of N particles which interact via pair forces. Achieving reversibility in a description of particle motion that is akin to Brownian motion, represents a salient point of the derivation. We demonstrate that certain objections raised against Nelson's theory are without substance. We also try to put the particular worldview of this version of stochastic quantum mechanics into perspective with regard to the established Copenhagen interpretation. [source]

A probabilistic approach to quantum mechanics based on ,tomograms'

FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7 2006
M. Caponigro
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation of quantum states. This can be regarded as a classical-like formulation of quantum mechanics which avoids the counterintuitive concepts of wave function and density operator. The relevant concepts of quantum mechanics are then reconsidered and the epistemological implications of such approach discussed. [source]

Heisenberg uncertainty relations can be replaced by stronger ones

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 8 2009
L. Skála
Abstract Two uncertainty relations, one related to the probability density current and the other one related to the probability density, are derived and discussed. Both relations are stronger than the Heisenberg uncertainty relations. Their generalization to the multidimensional case and to the mixed states is also discussed. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source]