PHYSICS 002C
Lecture 23
May 22, 2009
Serway and Jewett Chapter 28 – Quantum Mechanics
Review Chap 28.13
–
Blackbody radiation, the photo & Compton effects
proved beyond doubt that light comes in little packets of energy
hf
E
and
somehow is able to exhibit wavelike interference effects.
Review Chap 28.4,5
–Electron diffraction
experiment
of Davisson and
Germer proves that electrons are able to exhibit wavelike interference effects,
verifying de Broglie’s (1922) hypothesis correct 
p
h
/
.
WaveParticle duality
Today
–Probability amplitudes, wave functions, tunneling and
uncertainty
Chap 28.6
The quantum particle
What is an electron? is answered by what we can measure about it.
Internal properties:
Charge
1.602 176 46
10
19
C
Mass
9.109 381
10
31
kg
“Radius”
<10
17
m
Spin angular momentum
2
1
Magnetic moment
928.476 4
10
26
JT
1
Lepton number
+1
Compton wavelength
2.426 310 22
10
12
m
gfactor
2.002 319 304 374
External properties
Position (x,y,z)
Velocity
Momentum
Angular momentum
Kinetic Energy
We know we are observing an electron if we detect something with some of
the stated internal properties, charge and mass being sufficient.
Suppose an electron has been produced in a known state with momentum
p
.
As long as the electron does not interact with anything after its production, all
we know is
p
.
Where might the electron be found if we measure
x
?
If we don’t measure
is the electron at some particular point? No!
x
The first postulate of quantum mechanics is that the state of any quantum
system (like an electron) is specified by a complex probability amplitude, the
absolute square of which gives you the probability for measuring something.
1
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View Full DocumentThe picture of diffraction is the same whether you have a beam of photons or
electrons. A probability amplitude describing a plane wave traveling in the
x
direction
)}
(
exp{
)
(
t
kx
i
x
passes through a grating and becomes a
different probability amplitude wave as it nears the screen. When it interacts
with the screen, the local phases of the original wave are hopelessly scrambled
with the zillions of degrees of freedom of the screen (atomic vibrations,
electron motions). Averaging over all these phases leaves us with only the
probability
2
)
(
)
(
y
y
P
SCREEN
.
After the interaction with the screen (i.e. the measurement) the different parts
of the old electron wave function can no longer interfere with each other and
the electron is definitely located somewhere.
How do the other parts of the wave function know to vanish when you
detect an electron? The situation is more startling in the following
experiment.
Measurement of Correlated variables and the EinsteinPadolsky
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 Spring '08
 ALL
 Physics, Energy, Light, Radiation, Uncertainty Principle, Probability amplitude, probability amplitude wave

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