User:Boris Tsirelson/Sandbox1: Difference between revisions

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In [[Newtonian mechanics]], coordinates of moving bodies are functions of time. For example, the classical equation for a falling body; its height at a time ''t'' is
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:<math> h(t) = h_0 - \frac12 g t^2 </math>
The [[Heisenberg Uncertainty Principle|Heisenberg uncertainty principle]] for a particle does not allow a state in which the particle is simultaneously at a definite location and has also a definite momentum. Instead the particle has a range of momentum and spread in location attributable to quantum fluctuations.
(here ''h''<sub>0</sub> is the initial height, and ''g'' is the [[acceleration due to gravity]]). The height changes in time, but the function ''h'' does not.


{{Image|Moving wave.gif|right||<small>Fig. 5. Linear combination of lowest 3 modes </small> }}
An uncertainty principle applies to most of quantum mechanical operators that do not commute (specifically, to every pair of operators whose commutator is a non-zero scalar operator).
The instantaneous shape of a vibrating string is described by a function (the displacement is a function of the coordinate), and this function changes in time.

Latest revision as of 02:25, 22 November 2023


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The Heisenberg uncertainty principle for a particle does not allow a state in which the particle is simultaneously at a definite location and has also a definite momentum. Instead the particle has a range of momentum and spread in location attributable to quantum fluctuations.

An uncertainty principle applies to most of quantum mechanical operators that do not commute (specifically, to every pair of operators whose commutator is a non-zero scalar operator).

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