The probability will depend on the
free choice of the experimenter as to which "observables" to look for/ This depends on the measurement apparatus design. For example, if the measurement apparatus can register
n discrete
eigenvalues,
ψ can be expanded in terms of a set of
n eigenfunctions appropriate for the chosen observable, say
φn.
The expansion is then
ψ = ∑ cn φn,
and we say the system is in a "superposition" of these n states.
When the absolute squares of the coefficients cn are appropriately normalized to add up to 1, the probability Pn of observing value n is
Pn = cn2 = | < ψ | φn > | 2
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