Heisenberg uncertainty relation and statistical measures in the square well

Heisenberg uncertainty relation and statistical measures in the square well

A non stationary state in the one-dimensional infinite square well formed by a combination of the ground state and the first excited one is considered. The statistical complexity and the Fisher-Shannon entropy in position and momentum are calculated with time for this system. These measures are compared with the Heisenberg uncertainty relation, ∆x∆p. It is observed that the extreme values of ∆x...

Generalizations of Heisenberg Uncertainty Relation *

A survey on the generalizations of Heisenberg uncertainty relation and a general scheme for their entangled extensions to several states and observables is presented. The scheme is illustrated on the examples of one and two states and canonical quantum observables, and spin and quasi-spin components.

Heisenberg Uncertainty Relation in Quantum Liouville Equation

We consider the quantum Liouville equation and give a characterization of the solutions which satisfy the Heisenberg uncertainty relation. We analyze three cases. Initially we consider a particular solution of the quantum Liouville equation: the Wigner transform f x,v,t of a generic solution ψ x;t of the Schrödinger equation. We give a representation of ψ x, t by the Hermite functions. We show ...

Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems

The D-dimensional harmonic system (i.e., a particle moving under the action of a quadratic potential) is, together with the hydrogenic system, the main prototype of the physics of multidimensional quantum systems. In this work, we rigorously determine the leading term of the Heisenberg-like and entropy-like uncertainty measures of this system as given by the radial expectation values and the Ré...

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