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waves and uncertainty Prof. Stephen Sekula (2/16/2010) Supplementary Material for PHY 3305 (Modern Physics) Harris, Ch. 4.4-4.5, 5.1-5.2

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waves and uncertainty

Prof. Stephen Sekula(2/16/2010)

Supplementary Material for PHY 3305 (Modern Physics)Harris, Ch. 4.4-4.5, 5.1-5.2

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table of contents

● Review● Plane waves as “lego mindstorms”● single-slit diffraction and certainty

● varying slit width, momentum, and position

● uncertainty in energy and time● LEP and the Z boson

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Review

● We moved to a wave description of nature● particle and wave behavior (in a measurement sense) is recovered for different “relevant dimensions”

● The wave nature is described by the Schroedinger Wave Equation (SWE)● Like energy conservation or F=ma, it is derived from observations of nature and cannot be constructed from “first principles”

● We discussed complex numbers and functions

● We discussed the meaning of the “wave function”, (x,t)ψ

● it describes PROBABILITY DENSITY (per unit length in 2-D, per unit volume in 3-D)

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Atoms

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Stephen J. Sekula - SMU 5

PLane Wave

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Stephen J. Sekula - SMU 6

Quantum wave demonstration

http://phet.colorado.edu/simulations/sims.php?sim=Quantum_Tunneling_and_Wave_Packets

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Stephen J. Sekula - SMU 7

Making waves

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Stephen J. Sekula - SMU 8

diffraction and certainty

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Stephen J. Sekula - SMU 9

Varying the slit width (w)

Red: w = λGreen: w = 10 λBlue: w = 50 λ

Inte

n sity

(Pro

babil it

Angle (radians)

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Stephen J. Sekula - SMU 10

LEP and ALEPH at CERN

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Stephen J. Sekula - SMU 11

Mass of subatomic particles

Measurement of the width of the Z boson by the ALEPH experiment

(Published in Eur.Phys.J.C14:1-50,2000)

Uncertainties on the collider energy were ~1000 times smaller than the width of the Z seen here!

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Stephen J. Sekula - SMU 12

Next Time

● “Particle in a Box”● illustrates a first approach to solving for the spatial wave function, (x)ψ

● Reading: Harris 5.3-5.5

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