4/7/2004
H133 Spring 2004
1
Chapter 6
•
We have explored the some of the evidence that led to
the formulation of quantum mechanics. Now we need to
start to develop the mathematic model for quantum
mechanics which will allow us to explain the
experiments we have discussed.
•
We are going to take the following approach
Develop a set of rules for quantum mechanics. We will
accept these rules as correct
Define something called a “Wavefunction”. This is the key
function (discrete and continuous) that define the state of
our system.
We will see how the rules and the wavefunction allow us
to predict our observations with SG devices and with the
two-slit experiment with particles.
•
Note: Quantum Mechanics is not like the other theories
that we have studied in the past. In quantum mechanics
the mathematical model makes a direct connection to
the observation.
We don’t have a conceptual models or
examples to help form a intuition about what is
happening. That’s just something we will have to live
with in the strange world of quantum mechanics.
Special Note: Professor Heinz may start lecturing
on this chapter. He may not necessarily follow
these notes.
I will finish this chapter.

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4/7/2004
H133 Spring 2004
2
“Observables”
•
All quanta have a set of
intrinsic characteristics
that
help define what that object is
Mass, Electric charge, Spin, etc.
These never change for a particle and it is these
quantities that define the particle.
An electron is an object with mass 0.511 MeV/c
2
,
-1 electric charge, and spin of ½ .
•
All quanta also have a set of quantities which we call
“observables”, which we can measure experimentally.
Position, Momentum, Energy, Spin Projection
We will deal mostly with these…but there are others too.
When we perform and experiment these are the quantities
we normally determine and by measuring these we can
often extract the
intrinsic
characteristics.
•
We will divide “observables” into two different groups
Spin Subset
(S
x
, S
y
, S
z
)
Position Subset
(x, p)
Included in these subsets are other variables that can be
determined from the basic components of the subset.
e.g.
E = p
x
2
/2m + V(x)
can be determined from x, p.
Normally, these two subsets are independent of one
another and therefore we can consider one at a time.