A state is expanded in the eigenfunctions of some Hermitian operator

PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · The formalism of quantum mechanics · The formalism of quantum mechanics

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Observables, commutators and the uncertainty relations

Problem

A state is expanded in the eigenfunctions of some Hermitian operator Q^\hat Q, with eigenvalues q1=1q_1 = 1, q2=2q_2 = 2, q3=3q_3 = 3 (in some fixed unit) and coefficients c1=35c_1 = \tfrac35, c2=45ic_2 = \tfrac{4}{5}i, c3=0c_3 = 0. Find the probability of each possible outcome of a measurement of QQ, check that they add to one, and find ⟨Q⟩\langle Q\rangle.

Related theory

Browse the problem library