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  About site: http://zebu.uoregon.edu/~imamura/208/jan27/hup.html

Title: Physics/Quantum Mechanics/Resources - Heisenberg Uncertainty Principle An explanation of Heisenberg's Uncertainty Principle along with an applet demonstrating the law. The applet also allows for a user-defined momentum distribution.
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Heisenberg Uncertainty Principle

Heisenberg Uncertainty Principle

An odd aspect of Quantum Mechanics is contained in theHeisenbergUncertainty Principle (HUP). The HUP can be stated in differentways, let me first talk in terms of momentum and position.If there is a particle, such as an electron, moving through space, I cancharacterize its motion by telling you where it is (its position) and what its velocity is (more precisely, its momentum). Classically, that is, in our macroscopic world, I could, in principle, measurethe position and momentum of the object to infinite precision (more or less). There is really no question about a particle's position and momentum.In the Quantum Mechanical world, the idea that we can locate objects exactly breaks down. Let me state this idea more precisely. Suppose a particle has momemtum p and position x. In a Quantum Mechanical world, I would not be able to measure pand x precisely. There would be an uncertainty associated witheach measurement that I could never get rid of, even in a perfect experiment!!!The size of the uncertainties are not independent; they are related aswhere the symbol on the right hand side of the inequality, the h with a slash through it is known as "h bar" and represents the Planck constant h divided 2 pi.The above is a statement of the Heisenberg UncertaintyPrinciple. A consequence of the Uncertainty Principle is that if an object's position x is defined precisely then themomentum of the object will be only weakly constrained, and vice versa.One cannot simultaneously find both the position and momentum of an object to arbitrary accuracy.This uncertainty leads to some strange effects. For example, ina Quantum Mechanical world, I cannot predict where a particlewill be with 100 % certainty. I can only speak in terms of probabilities.For example, I can only say that an atom will be at some location with a 99 % probability, and that there will be a 1 % probability it will be somewhere else (in fact, there will be a small but finite probabilty that it can even be found acrossthe Universe). This is strange.We do not know if this indeterminism is actually the way the Universe works, because the theory ofQuantum Mechanics is probably incomplete. That is, we do notknow if the Universe actually behaves in a probabilistic manner (there are many possible paths a particle can follow and the observed path is chosen probabilistically) or if the Universeis deterministic in the sense that I could predict thepath a particle will follow with 100 % certainty.A consequence of the Quantum Mechanical nature of the world isthat particles can appear in places where they have no right to be (from an ordinary, common sense [classical] point of view)!This has interesting consequences for nuclear fusion in stars.
 

An

explanation

of

Heisenberg's

Uncertainty

Principle

along

with

an

applet

demonstrating

the

law.

The

applet

also

allows

for

a

user-defined

momentum

distribution.

http://zebu.uoregon.edu/~imamura/208/jan27/hup.html

Heisenberg Uncertainty Principle 2009 January

dvd rental

dvd


An explanation of Heisenberg's Uncertainty Principle along with an applet demonstrating the law. The applet also allows for a user-defined momentum distribution.

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