8.04 Quantum Physics
Lecture V
Last time
| (x)|2 and |(k )|2 as probability densities in position and momentum space,
respectively. . .
Parsevals theorem: dx| (x)|2 = dk |(k )|2
Normalization: 1= dx| (x)|2 = dk |(k )|2
Measurement:
Measurement
8.04 Quantum Physics
Lecture IV
Last time
Heisenberg uncertainty xpx
h
2
as diraction phenomenon
Fourier decomposition
1
(x) =
dk(k )eikx
2
1
h
=
dp(p)eipx/
2h
1
(p) = (k )
h
(4-1)
(4-2)
Today
how to calculate (k )
interpretation of (x) and
8.04 Quantum Physics
Lecture III
Last time we discussed
boundary between CM and QM set by resolution of measurement apparatus
in phase space
transition between CM and QM
Fermats principle of stationary time
Light takes the path where there is no rst
8.04 Quantum Physics
Lecture II
CM fails to describe macroscopic quantum phenomena. Phenomena where micro
scopic properties carry over into macroscopic world:
superuidity
Helium ows without friction at suciently low temperature.
superconductivity
Cur
8.04 Quantum Physics
Lecture I
Lecturer
Vladan Vuletic
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due following Thursday afternoon
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