Transcript Torres: 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!
COPENHAGEN QUANTUM MECHANICS
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?
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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
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 particle
Fundamental equation of ALL
quantum mechanics
Güten tag.
ich heiße
Erwin
Schrödinger
A CLOSER LOOK
iħ=( )(reduced Planck’s constant)
 d/dt = Time derivative
 Ψ(r,t) = Wave function
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= Laplacian function
 V(r,t)= Potential Energy
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CLASSICAL VERSUS QUANTUM
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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
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
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Objects move through
barriers
Probability to find the
wavefunction on the
opposite side of the
barrier is not zero
HYDROGEN ATOM
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Probable positions of
electrons are not exactly
set
Based on energy levels
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
THE UNCERTAINTY PRINCIPLE?
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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
BOHR EINSTEIN DEBATES
God
does
not play
dice.
Stop
telling God
what to
do.
EINSTEIN’S BOX- 1930
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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
THE DOUBLE SLIT EXPERIMENT
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http://tinyurl.com/yzttx3
Wave particle duality
Electrons interfere with
themselves as waves but
strike the detector as
particles