If the wave function describing a system is not an eigenfunction of the operator B, measurements on

If the wave function describing a system is not an eigenfunction of the operator Bˆ, measurements on identically prepared systems will give different results. The variance of this set of results is defined in error analysis as σ²_B = 〈(B − 〈B〉²〉 where B is the value of the observable in a single measurement and (B) is the average of all measurements. Using the definition of average value from the quantum mechanical postulates, (A) = ʃψ^*(x) Âψ(x) dx, show that σ²_B = (B²) – (B)².