
The Essentials of Quantum Mechanics 53
can capture this process by some measurement operator
ˆ
M
A
acting on
the state, then we must have
ˆ
M
A
|ψi =
|aiha|ψi
|ha|ψi|
2
.
But such an operator cannot be defined independent of |ψi. Measurements
must thus have a separate status in quantum mechanics, and the process is
not represented by a unitary operator. This is the meaning of the second
measurement postulate.
What is the value of an observable in a quantum state?
Someone gives you an electron and asks you: what is the spin? How will
you answer? If you measure S
x
, S
y
, or S
z
you will get one of two answers, at
random. Any observable you measure gives one of its eigenv ...