Physics · Advanced university
Expectation value in an orthogonal eigenbasis · formula reference
The squared amplitudes are probabilities. Orthogonality and normalization are specified.
Formula
The squared amplitudes are probabilities. Orthogonality and normalization are specified.
⟨A⟩ = Σ |cj|² aj
Worked example
A normalized state has probabilities 0.3 and 0.7 for two orthogonal eigenstates of A with eigenvalues -4 and 18. Calculate ⟨A⟩. Round the final result to 4 decimal places if needed.
The expectation is the probability-weighted sum 0.3(-4) + (1−0.3)(18).
11.4
Prerequisites and checking
Algebra, calculus and the stated physical model. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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