Find the (a) Normalization constant, N, (b) the expectation value of the observables <Ô>, (c) σo, and (d) the probability of finding the eigen value "a" in a measurement for the following wave functions:
ψ=N(2φ1+φ2+φ3),
Where φ1, φ2, φ3 are three orthonormal eigenfunctions of the operator Ô with eigen values (a is a numerical constant)
Ôφ1=aφ1, Ôφ2=3aφ2, Ôφ3=5aφ3