Editing Indistinguishable particles (section)

=== Measurement ===

Suppose there is a system of ''N'' bosons (fermions) in the symmetric (antisymmetric) state
: <math>|n_1 n_2 \cdots n_N; S/A \rang</math>
and a measurement is performed on some other set of discrete observables, ''m''. In general, this yields some result ''m''<sub>1</sub> for one particle, ''m''<sub>2</sub> for another particle, and so forth. If the particles are bosons (fermions), the state after the measurement must remain symmetric (antisymmetric), i.e.
: <math>|m_1 m_2 \cdots m_N; S/A \rang</math>

The probability of obtaining a particular result for the ''m'' measurement is
: <math>P_{S/A}\left(n_1, \ldots, n_N \rightarrow m_1, \ldots, m_N\right) \equiv \big|\left\lang m_1 \cdots m_N; S/A \,|\, n_1 \cdots n_N; S/A \right\rang \big|^2 </math>

It can be shown that
: <math>\sum_{m_1 \le m_2 \le \dots \le m_N} P_{S/A}(n_1, \ldots, n_N \rightarrow m_1, \ldots, m_N) = 1</math>
which verifies that the total probability is 1. The sum has to be restricted to ''ordered'' values of ''m''<sub>1</sub>, ..., ''m<sub>N</sub>'' to ensure that each multi-particle state is not counted more than once.