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Commutation of Operators
•
Since operators are matrices, they do not
necessarily commute
•
We define the commutator of the operators
A and B as
BA
AB
!
[
]
BA
AB
B
A
!
=
,
Lecture 4: Postulates of QM
•
Quantum mechanics underlies Nuclear,
Particle, Condensed Matter, and Atomic
physics (and is thus very important for
Astronomy and Astrophysics)
•
Quantum mechanics explains the periodic
table and Chemistry
•
When tested, Quantum Mechanics has
always been found to be correct
–
Some predictions of QM tested to ten
decimal places of precision
•
Quantum Mechanics is selfconsistent,
there are no ‘paradoxes’
–
So called ‘paradoxes of QM’ are merely
points where its predictions conflict with
‘classical’ intuition about the nature of reality
•
The ‘meaning’ of Quantum Mechanics is not
‘understood’
–
The key difficulty is the origin of the
randomness inherent in QM
–
Is true randomness logically tenable?
–
Very different interpretations are equally
valid
•
Manyworlds, Bohmian mechanics,…
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View Full DocumentQuestion #1
•
Suppose a particle has the wavefunction:
•
If the position of the particle is measured,
what will the result of the measurement be?
2
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 Fall '08
 MichaelMoore
 mechanics

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