- #1
foxjwill
- 354
- 0
Homework Statement
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.
Homework Equations
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?