The Heisenberg Relation - Mathematical Formulations
نویسندگان
چکیده
منابع مشابه
The Heisenberg Relation – Mathematical Formulations
We study some of the possibilities for formulating the Heisenberg relation of quantum mechanics in mathematical terms. In particular, we examine the framework discussed by Murray and von Neumann, the family (algebra) of operators affiliated with a finite factor (of infinite linear dimension).
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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 ...
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We study the consequences of the generalized Heisenberg uncertainty relation which admits a minimal uncertainty in length such as the case in a theory of quantum gravity. In particular, the theory of quantum harmonic oscillators arising from such a generalized uncertainty relation is examined. We demonstrate that all the standard properties of the quantum harmonic oscillators prevail when we em...
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Uncertainty is unavoidable in any statistical modelling due to finite sets of samples and random noise in measurements. Bayesian probability theory offers an elegant and consistent way to handle this lack of absolute confidence by representing the experimenter’s uncertainty explicitly in the form of probability distributions. The inference process begins at the description of what would be obse...
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ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2014
ISSN: 1815-0659
DOI: 10.3842/sigma.2014.009