Position Uncertainty in the Heisenberg Uncertainty Relation

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 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...

Position measuring interactions and the Heisenberg uncertainty principle

Measurements disturb microscopic objects inevitably. The problem still remains open as to how measurements disturb their objects. It is frequently claimed that if one measures position with noise , the momentum is disturbed at least h̄/2 [1, p. 230]. This claim is often called the Heisenberg uncertainty principle. The Heisenberg principle has been demonstrated typically by a thought experiment u...

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