We can use this apparatus toprepare an eigenstate. The apparatus below picks out them= 1
state
N
S
S
S
N
N
+
0 |
−|
z→
again representing the apparatus by the symbol at the right. We could also represent our apparatus
plus blocking by an operator
O=|+〉〈+|where we are writing the states according to themvalue, either +, -, or 0. This is a projection
operator onto the + state.
An apparatus which blocks both the + and - beams
N
S
S
S
N
N
+|
0
−|
z→
would be represented by the projection operator
O=| 0 〉〈 0 |Similarly, an apparatus with no blocking could be written as the sum of the three projection oper-
ators.
+
0
−
z→=|+〉〈+| + | 0 〉〈 0 | + |−〉〈−|=
∑+1
m=− 1|zm〉〈zm|= 1