wave nature of radiation and matter
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ScientificMethod
Includes several interdependent steps:* Observations * Controlled Experiments
* Qualitative and Quantitative Reasoning Mathematical Modeling * Predictions
Verification/Falsification of Theories
Speculation and conjecture also have a placein science; but ultimately, an acceptablescientific theory must be verified by relevantobservations and experiments.
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Physics: Theory
Experiment Physics is a systematic attempt to
understand natural phenomena inas much depth and detail as
possible, and use this knowledge topredict, modify and controlphenomena.
Theories are constructed to explain
experimental facts Trying to answer the question
HOW (and not WHY) thingshappen in nature
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Evolution ofPhysics
Physics has a history of synthesizingmany phenomena into a few theories:
Newton
Maxwell
Motion
HeatSound
Light Electricity
Magnetism
Gravity
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Recap: ClassicalMechanics
Newtons laws of Motion:
Second Law Measures The Force
F=ma
Equation of motion:
M d2x/dt2 = Force
F=Mg [Gravitational Force]
F=Q[E+VxB] { LorentzForce}Job: x(t), given x(0).
Deterministic
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Relativity
Theory of how physicsTheory of how physics
will appear to differentwill appear to differentobservers who areobservers who are
moving at somemoving at some
uniform velocity withuniform velocity withrespect to one another.respect to one another.
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What is Light?
Newton: Light was made up of particles
(corpuscles)
He was right, but the reasoning thathe used to come to that decision was
erroneous.
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Wave Theory OfLight
Huygens Concept of LightWaves.
Maxwell's Equations
Interference Diffraction
Polarization
Light waves part ofElectromagnetic Spectrum.
Now we use light for
communication
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Particle Effect
Einstein (1905): The photoelectriceffect was thought to be the mostdirect and convincing evidence ofthe existence of photons and the'corpuscular' nature of light and
electromagnetic radiation.
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The Nobel Prize inPhysics 1921
for his services to TheoreticalPhysics, and especially for his
discovery of the law of thephotoelectric effect.
Einstein (1879 1955)
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OtherExperiments
Compton Effect.
X-ray Production.
Pair-Production.
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What is Light?Waves!
Partial Reflection 4% of the photons
are reflected by the front surface of aglass slab while the other 96% are
transmitted into.Difficulty: How does a single photon
know which of the two possiblepaths it should take when it hits the
glass surface?How does it make up its mind?DEEP MYSTERY!!
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What is Light??
Newtons corpuscular theory was notsatisfactory. Partial Reflection could beexplained by a theory of waves, but the wavetheory could not explain Photoelectric Effect.
So there was a period inwhich one had to know whichexperiment one was analyzingin order to tell if light was
waves or particles. This stateof confusion was called theWave-Particle Duality oflight !
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Quantum Optics
Light was waves on Mondays,Wednesdays and Fridays; it was particleson Tuesdays, Thursdays and Saturdays;
and on Sundays, we think about it!
Quantum Optics reconciles the particleproperties of light with the wave nature.
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Wave Properties ofParticles
In 1924, Louis de Broglie postulated thatbecausephotons have wave and particlecharacteristics, perhaps all forms of matterhave both properties
For instance, for a photon:
De Broglie suggested that this formula istrue for any particle! Thus, the frequencyand wavelength of matter waves can bedetermined. I.e. de Broglie wavelength of aparticle is
h
mv
hc E hf
E hc hp
c c thus or
h
p
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Wave Properties of
Particles The frequency of matter wavescan also be determined
E
h
E hf
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The Davisson-Germer
Experiment They scattered low-energy electrons from a nickel target
They followed this with extensive diffraction
measurements from various materials
The wavelength of the electrons calculated fromthe diffraction data agreed with the expected deBroglie wavelength
This confirmed the wave nature of electrons
Other experimenters have confirmed the wave nature ofother particles
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The Electron Microscope
The electron microscopedepends on the wavecharacteristics of electrons
Microscopes can onlyresolve details that areslightly smaller than thewavelength of theradiation used to
illuminate the object The electrons can be
accelerated to highenergies and have smallwavelengths
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Birth of QuantumMechanics
Electron Theory of Matter (1900):
Electrons + Nucleus Failure ofClassical Laws
Quantum Mechanics (1926-27Schroedinger, Heisenberg, Born):
Nonrelativistic
Invented to explain the strange andclassically inexplicable behavior ofatoms and molecules thespectrum of light they emitted
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The Wave Function
In 1926 Schrdinger proposed a waveequation that describes the manner inwhich matter waves change in space andtime
Schrdingers wave equation is a keyelement in quantum mechanics
Schrdingers wave equation is generallysolved for the wave function,
The wave function depends on theparticles position and the time
i Ht
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The WaveFunction
The value of ||2 at some
location at a given time isproportional to the probabilityof finding the particle at thatlocation at that time
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QuantumMechanics
1. The question how a photon choosesits path given some alternative isoperationally meaningless.
All we can predict from theory is thatout of 100 photons that come down,an average of 4 will be reflected bythe front surface.
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The UncertaintyPrinciple
When measurements are made, theexperimenter is always faced withexperimental uncertainties in the
measurements
Classical mechanics offers no fundamental barrier toultimate refinements in measurements
Classical mechanics would allow for measurementswith arbitrarily small uncertainties
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The UncertaintyPrinciple Quantum mechanics predicts that a barrier to
measurements with ultimately small uncertaintiesdoes exist
In 1927 Heisenberg introduced the uncertaintyprinciple
If a measurement of position of a particle is made withprecision x and a simultaneous measurement of linearmomentum is made with precision p, then the productof the two uncertainties can never be smaller than h/4
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The UncertaintyPrinciple
Mathematically,
It is physically impossible to
measure simultaneously the exactposition and the exact linearmomentum of a particle
Another form of the principle deals
with energy and time:
4
hpx x
4
htE
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Thought Experiment the Uncertainty Principle
A thought experiment for viewingan electron with a powerfulmicroscope
In order to see the electron, at
least one photon must bounce offit During this interaction,
momentum is transferred from thephoton to the electron
Therefore, the light that allowsyou to accurately locate theelectron changes the momentumof the electron
Q
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QuantumMechanics
QM demanded a wholechange in philosophy:
Determinism of classical physics QMpredictability which can at best beprobabilistic, with an intrinsic indeterminacy
(Uncertainty Principle) Conceptual Problems...
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QuantumMechanics
Physics has beenreduced to calculatingonly the probability of an
event, and not predictingexactlywhat will happen!!
Nature permits us to
calculate onlyprobabilities.
Quantum
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QuantumMechanics
This crazy model of the world can explainall the simple properties of light --Light goes in straight lines;When light reflects off a mirror, the
angle of incidence is equal to the angleof reflection;Refraction;Interference;
Diffraction;and so on...
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Where to?
Superposition principle Schroedingers cat paradox
Against common sense buthas no experimental doubtabout it.
Use the superposition stateto build a Quantum
Computer?!Immense parallel-processingmachine
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Where to?Atomic Physics.
Interaction betweenmatter /radiation
Super fluids
SuperconductorsSemiconductor Physics
Condensed matter Physics
Nuclear and particle PhysicsNano-Physics
Computational Physics
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Our Group:
Testing Quantum Mechanics atLow Energy .
Studying Nuclear Structure. Extreme case of neutron and
proton rich light nuclei. Our Recent Contribution Phys Rev C 77 014303 APS
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Moral of thestory
Theory ExperimentApplications
Scientific Methods continue!
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Than
ks