Let the system be in a state \(\psi\) which is not an Eigenstate of the operator
\(A\).
The expectation value has according to axiom 4 no sharp value, i.e. each
Eigenvalue of \(A\) may occur when performing a measurement.
Measuring means
to create conditions under which the system
has to decide which of the possible sharp values a of the operator \(A\) is found.
A good Measurement
only filters out one special Eigenvalue \(a_k\) out of a mixture of the Eigenstates of the operator \(A\). The probability to find \(a_k\)
is \(c_k^*c_k\).
A bad Measurement
changes the Hamiltonian of the system.
Measuring implies
to change the state.
”It is impossible just
to look at a quantum mechanical particle!”
Measuring should be understood as
- the projection of a state
into the system of Eigenvectors of an operator + decision in favor of one component.
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© J. Carstensen (Quantum Mech.)