1. The problem statement, all variables and given/known data On page 5 of http://arcsecond.wordpress.com/2009...uality-and-heisenbergs-uncertainty-principle/ the author states (w/o proof) that if [tex]\psi[/tex] is an eigenvector (say with eigenvalue [tex]\lambda[/tex]) of an Hermitian operator A (I don't think the Hermitian-ness matters here), then its variance is 0; that is, [tex]\langle \psi| A^2\psi\rangle = \langle \psi| A\psi\rangle^2[/tex]. However, I've not been able to show this. 2. Relevant equations 3. The attempt at a solution I keep getting [tex]\langle \psi|A^2\psi\rangle = \lambda\langle \psi|A\psi\rangle = \lambda^2\langle\psi |\psi\rangle[/tex]and [tex]\langle \psi|A\psi\rangle^2 = \left(\lambda\langle \psi|A\psi\rangle\right)^2 = \lambda^2\langle\psi |\psi\rangle^2.[/tex]Where am I going wrong?