Heisenberg: Mathematics is sense! That’s what sense is! Bohr: But in the end, in the end,...
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Transcript of Heisenberg: Mathematics is sense! That’s what sense is! Bohr: But in the end, in the end,...
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COPENHAGEN QUANTUM MECHANICS
Heisenberg: Mathematics is sense! That’s what sense is!Bohr: But in the end, in the end, remember, we have to be able to explain it all to Margrethe!
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PEOPLE REVIEW
Max Plank 1858-1947 Albert Einstein 1879-1955 Neils Bohr 1885-1962 Werner Heisenberg 1901-1976 Erwin Schrödinger 1887-1961
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WHAT IS QUANTUM, AND IS IT AS BAD AS THE JAMES BOND FILM?
A Quantum is defined as the smallest bit of anything
Quantum Mechanics= Mechanics of the very small
Not even science can explain how terrible Quantum of Solace was
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SOME SIMPLE QUANTUM MECHANICAL SYSTEMS
Special Relativity- E2=p2c2+m2c4
Planck- E=hf For a massless particle, E=pc ʎf=c Gives us: ʎ=h/p Early 20s, deBroglie proposed that any
mass would correspond to a wavelength 1929, deBroglie Nobel Prize
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1926, Erwin Schrödinger creates equation that predicts this wave deBroglie predicted Ψ(x,y,z,t)Could be used for any particleFundamental equation of ALL quantum mechanics
Güten tag.ich heiße Erwin Schrödinger
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A CLOSER LOOK
iħ=( )(reduced Planck’s constant) d/dt = Time derivative Ψ(r,t) = Wave function = Laplacian function V(r,t)= Potential Energy
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CLASSICAL VERSUS QUANTUM
http://tinyurl.com/c8t3e94
Classical: A Quantum: B-F Probability to find the particle in any
one spot is equal classically and particle can have any value
Probability to find the particle in any one spot is not equal at the quantum level
Confines wavelength to ʎn=2l/n
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INTERPRETATIONS OF THE WAVE FUNCTION
Interpretation 1: “Ok, wow, that’s kinda gross”
Interpretation 2: Calculus? Yes. Interpretation 3: “But Chris, what does
that imply?”
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TUNNELING
Objects move through barriers
Probability to find the wavefunction on the opposite side of the barrier is not zero
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HYDROGEN ATOM
Probable positions of electrons are not exactly set
Based on energy levels
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DISTINCTION BETWEEN LARGE AND SMALL
None of this could happen on the visible scale “it becomes important to remember that
science is concerned only with observable things and that we can observe an object only by letting it interact with some outside influence” -Dirac
This interaction, observation, causes a disturbance on the quantum scale
Traditional causality only applies to undisturbed systems
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NO CATS WERE HARMED IN THE MAKING OF THIS PHYSICS
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THE UNCERTAINTY PRINCIPLE?
Werner Heisenberg 1925-1926
Values of position and momentum cannot both be precisely known.
Measuring one with greater precision lowers the accuracy of the other
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BOHR EINSTEIN DEBATES
God does not play dice.
Stop telling God what to do.
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EINSTEIN’S BOX- 1930
Box of mass “m” with a clock that controls a shutter
Box releases a photon in some arbitrary time t creating a change in mass
E=mc2 gives precise energy
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THE DOUBLE SLIT EXPERIMENT
http://tinyurl.com/yzttx3
Wave particle duality
Electrons interfere with themselves as waves but strike the detector as particles