Transcript
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Quantum Mechanics for
Scientists and Engineers
David Miller
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Introduction to quantum mechanics
Lilght
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Black-body spectrum
Output power (per unit
wavelength)For a black body at 5800K
approximately like the sun
For a black body at 3000Kapproximately like anincandescent light bulb
Wavelength (nm)
500 1000 1500 2000
Power/unit
wavelength
(arbitra
ryunits)
0
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Black-body spectrum
Visible light spectrum
For a black body at 5800Kapproximately like the sun
For a black body at 3000K
approximately like anincandescent light bulb
Wavelength (nm)
500 600 700
Power/unit
wavelength
(arbitra
ryunits)
400
x 25
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Black-body spectrum
Output power (per unit
wavelength)For a black body at 5800K
approximately like the sun
The Rayleigh-Jeans classicalmodel gives theultra-violet catastrophe
showing no good
explanation for theshape of the curve Wavelength (nm)
500 1000 1500 2000
Power/unit
wavelength
(arbitra
ryunits)
0
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Light is emitted in quanta of
energy
where (Greek letter nu)
is the lights frequency inHz (Hertz) andh is Plancks constant
J s(Joule seconds)
Plancks proposal
E h
34
6.62606957 10h
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VI-+
Metal
plate
Light
Flow of
negativecharge
Collecting
plate
Photoelectric effect
Shining ultraviolet light on the
metal plategives flow of negative charge(Hertz, 1887)
Flow can be stopped with aspecific voltageindependent of thebrightness
but dependent only on thefrequency (Lenard, 1902)
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workfunction,
metal vacuum
electro
nenergy
pool of
electronsin metal
photonenergy,h
kinetic energy ofemitted electron
Photoelectric effect
Einsteins proposal (1905)
light is actually made up outof particlesphotons, of energy
The kinetic energy of theemitted electronsis the energy left over after
the electron has been
lifted over the workfunction barrier
E h
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Wave-particle duality
How can light simultaneously be
a wave and a particle?In the end, this is arguably not a problem for
quantum mechanics
we just need to avoid bringing along all theclassical attributes of particles and of wavesThe wave-particle duality of light is verified
trillions of times a day
in optical fiber communications
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Introduction to quantum mechanics
Matter
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H-alpha
656.3 nm
H-beta
486.1 nm
H-gamma
431.4 nm
H-delta
410.2 nm
Hydrogen atom emission spectra
Hot hydrogen emits lightin a set of spectral lines
Balmer seriesset of lines in the visible spectrum
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2
h
Bohr model of the hydrogen atom
A small negatively charged electronorbits a small positively charged
core (the proton)like a planet round a sun
but with electrostatic attractionKey assumption (Neils Bohr, 1913)
angular momentum is quantizedin units of Plancks constant, h,over 2
proton
electron
h bar
2n 1n
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2
h
Bohr model of the hydrogen atom
The model does give the photonenergies of the spectral linesas the separations of the
energies of the different orbits
proton
electron
h bar
1n 2n
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Hydro
genatome
nergy
n=2
n=3n=4
n=5n=6
H-alpha656.3 nm
n=3 ton=2
H-beta486.1 nm
n=4 ton=2
H-gamma431.4 nmn=5 to
n=2
H-delta410.2 nmn=6 to
n=2
Hydrogen atom emission spectra
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2
h
Bohr model of the hydrogen atom
The model
successfully introduces Plancksconstant into the theory ofmatter
gets the approximate size of theatom rightthe characteristic size is the
Bohr radius ~ 0.05 nm
0.5 (ngstrms)
proton
electron
h bar
1n 2n
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2
h
Bohr model of the hydrogen atom
The model does not get the angular
momentum quite rightthough the quantization inunits remains very important
It appears to predict the atom wouldradiate all the timefrom the orbiting electron
The atom does not look like this
it is not a small point electron ina classical orbit
proton
electron
h bar
1n 2n
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Hydrogen atom orbitals
4MM.3MM
n=1 n=2 l=1 m=1
Electron charge density in hydrogen orbitalsThe electron is not a moving point particle
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de Broglie hypothesis
A particle with mass
also behaves as a wavewith wavelength
wherep is the particlesmomentum
h
p
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Matrices and waves
Werner Heisenberg (1925)
matrix formulation ofquantum mechanics
Erwin Schrdinger (1926)wave equation
More key contributions byMax Born, Pascual Jordan,
Paul Dirac, John von
Neumann,
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Introduction to quantum mechanics
The usefulness of quantum mechanics
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Transistors and integrated circuits
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Transistors and gate tunneling
With smaller transistorsthe gate oxide becomes thinner
allowing quantum mechanical tunnelinggiving undesired gate leakage current
n+ n+
polysilicon
p
gate oxidechannel
GateSource Drain
silicon substrate
Tunneling current
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Introduction to quantum mechanics
Science, philosophy and meaning
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Reconstructing science
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What did you want to measure?
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Schrdingers cat
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More bizarre concepts
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Quantum mechanics works
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Using quantum mechanics
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