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UCSD
Physics 10
Quantum MechanicsQuantum Mechanics
Small things are weirdSmall things are weird
Spring 2008
2
UCSD
Physics 10
The Quantum Mechanics ViewThe Quantum Mechanics View
All matter (particles) has wave-like propertiesAll matter (particles) has wave-like properties
so-called particle-wave
duality
Particle-waves are described in a probabilistic mannerParticle-waves are described in a probabilistic manner
distribution describing where it might be foundelectron doesn’t whiz around the nucleus, it has a probability
allows for seemingly impossible “quantum tunneling”
Some properties come in dual packages: canSome properties come in dual packages: can’
’t know both
t know both
simultaneously to arbitrary precisionsimultaneously to arbitrary precision
called the Heisenberg Uncertainty Principle
not simply a matter of measurement precision
position/momentum and energy/time are example pairs
The act ofThe act of “
“measurement
measurement”
” fundamentally alters the system
fundamentally alters the system
called entanglement: information exchange alters a particle’s state
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3
UCSD
Physics 10
Crises in physics that demandedCrises in physics that demanded Q.M.
Q.M.
Why donWhy don’
’t atoms disintegrate in nanoseconds?
t atoms disintegrate in nanoseconds?
if electron is “orbiting”, it’s accelerating (wiggling)
wiggling charges emit electromagnetic radiation (energy)
loss of energy would cause prompt decay of orbit
Why donWhy don’
’t hot objects emit more ultraviolet t hot objects emit more ultraviolet
light than they do?light than they do?
hot bodynonsensical infinite energy radiating fromcatastrophe,” leading to obviouslyclassical theory suggested a “UV
father of quantum mechanics)postulating light quanta (now often called theMax Planck solved this problem by
Spring 2008
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UCSD
Physics 10
Pre-quantum problems, cont.Pre-quantum problems, cont.
materials, no matter how brightmaterials, no matter how brightWhy was red light incapable of knocking electrons out of certainWhy was red light incapable of knocking electrons out of certain
yet blue light could readily do so even at modest intensities
called the photoelectric effect
Einstein explained in terms of photons, and won Nobel Prize
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UCSD
Physics 10
Problems, cont.Problems, cont.
contain discretecontain discrete “What caused spectra of atoms toWhat caused spectra of atoms to
“lines lines”
could be emitted or absorbed by atomsoptical frequencies (wavelengths)it was apparent that only a small set of
Each atom has a distinctEach atom has a distinct “
“fingerprint fingerprint”
wavelengthswavelengthsLight only comes off at very specificLight only comes off at very specific
or frequencies
or energies
emits several wavelengthsemits several wavelengthsonly one electron and one proton,only one electron and one proton,Note that hydrogen (bottom), withNote that hydrogen (bottom), with
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6
UCSD
Physics 10
The victory of the weird theoryThe victory of the weird theory
designed and built:designed and built:Without Quantum Mechanics, we could never haveWithout Quantum Mechanics, we could never have
semiconductor devices
computers, cell phones, etc.
lasers
CD/DVD players, bar-code scanners, surgical applications
MRI (magnetic resonance imaging) technology
nuclear reactors
atomic clocks (e.g., GPS navigation)
Physicists didnPhysicists didn’
’t embrace quantum mechanics because it
t embrace quantum mechanics because it
was gnarly,was gnarly, novel, or weird
novel, or weird
it’s simply that the #$!&@ thing worked so well
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UCSD
Physics 10
LetLet’
’s start with photon energy
s start with photon energy
Light isLight is
quantizedquantized
into packets calledinto packets called
photonsphotons
Photons have associated:Photons have associated:
– frequency,
(nu)
– wavelength,
c
– speed,
c
(always)
– energy:
E
h
higher energy
more damaging
– momentum:
p
h
c
The constant,The constant,
hh
, is Planck, is Planck’
’s constant
s constant
– has
tiny
value of: h = 6.
J·s
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UCSD
Physics 10
How comeHow come
II’
’ve
ve
never seen a photon?never seen a photon?
Sunny day (outdoors):Sunny day (outdoors):
15
photons per second enter eye (2 mm pupil)
Moonlit night (outdoors):Moonlit night (outdoors):
10
photons/sec (6 mm pupil)
Moonless night (clear, starry sky)Moonless night (clear, starry sky)
8
photons/sec (6 mm pupil)
Light from dimmest naked eye star (mag 6.5):Light from dimmest naked eye star (mag 6.5):
– integration time of eye is about 1/8 sec– 1000 photons/sec entering eye
100 photon
threshold signal level
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UCSD
Physics 10
The Double Slit ExperimentThe Double Slit Experiment
particle?
wave?
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UCSD
Physics 10
ResultsResults
characteristic of wavescharacteristic of wavesThe pattern on the screen is an interference patternThe pattern on the screen is an interference pattern
So light is a wave, not particulateSo light is a wave, not particulate
But repeat the experiment one photon at a timeBut repeat the experiment one photon at a time
Over time, the photonsOver time, the photons
only landonly land on the
on the
interference peaksinterference peaks
, not in the troughs, not in the troughs
– pure ballistic particles would land in one of two spots– consider the fact that they also pile up in the middle!
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UCSD
Physics 10
Wave or Particle? Neither; Both; take your pickWave or Particle? Neither; Both; take your pick
Non-intuitive combination of wavelikeNon-intuitive combination of wavelike
andand
particle-likeparticle-like
individual photons, arriving one at a time.individual photons, arriving one at a time.intensity, see the interference pattern build up out ofintensity, see the interference pattern build up out ofAppears to behave in wavelike manner. But with lowAppears to behave in wavelike manner. But with low
How does the photonHow does the photon
knowknow
aboutabout “
“the other
the other”
” slit?
slit?
– Actually, it’s impossible to simultaneously observe
interference
and
know which slit the photon came through
– Photon “sees”, or “feels-out”
both
paths simultaneously!
Speak of wave-part describingSpeak of wave-part describing
probability distributionprobability distribution
of where individual photons may landof where individual photons may land
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UCSD
Physics 10
The hydrogenThe hydrogen atom
atom
levels in exact agreement withlevels in exact agreement with the optical spectrumis turned to the hydrogen atom, the solutions yield energyis turned to the hydrogen atom, the solutions yield energyWhen the mathematical machinery of quantum mechanicsWhen the mathematical machinery of quantum mechanics
the optical spectrum
where electrons can beEmergent picture is one of probability distributions describing
Probability distributions are staticProbability distributions are static
state” of probabilityelectron is not thought to whiz around atom: it’s in a “stationary
Separate functions describe the radial and angular patternSeparate functions describe the radial and angular pattern
http://hyperphysics.phy-astr.gsu.edu/hbase/hydwf.html
of quantum mechanicsfall out of the mathematicsobserved spectra, andhydrogen match the The energy levels of
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UCSD
Physics 10
The angular part of the storyThe angular part of the story
f d p s
quantum numberselectron. They are denoted within which one is likely to find an These plots describe the directions
l
and m, with
l
as the subscript and m as the
The superscript.
s state (
l
=0,m=0) is spherically
The finding in all directions.symmetric: equal probability of
p state can be most likely to
in the (1,1) state.and exactly the opposite situationat the equator) in the case of (1,0),find at the poles (and not at all
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Physics 10
do so classicallyenough energy todoes not haveeven though itside of the barrier,out on the otheroccasionally poprepelled, but willelectron usually repelled electron always
improbablebecomestunnelingwavelength,than the quantummuch thickerIf the wall isour daily lives?see tunneling inWhy do we not
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Physics 10
AssignmentsAssignments
References:References:
– Brian Greene’s
The Elegant Universe
has an excellent
ultraviolet catastrophe (among other quantum things)description/analogy of the quantum solution to the
– Chapter 31 isn’t half bad: read it for fun, even!
Assignments:Assignments:
– HW 7 due 5/30: 26.E.3, 26.E.4, 26.E.10, 26.E.14,– Read Hewitt pp. 566–572 on diffraction & interference– Read Hewitt chapters 30 & 31 (Quantum & Light)
questions available from website26.E.38, 26.P.4, 31.E.4, 31.E.9, plus 4 additional
