Homework Statement
An observable is represented by the matrix
0 \frac{1}{\sqrt{2}} 0
\frac{1}{\sqrt{2}} 0 \frac{1}{\sqrt{2}}
0 \frac{1}{\sqrt{2}} 0
Find the normalized eigenvectors and corresponding eigenvalues.
The Attempt at a Solution
I...
Homework Statement
A point charge q is located at the center of a dielectric sphere of radius a. Find D, E, and P everywhere and plot your results. What is the total bound charge on the surface of the sphere?
(I assume by "everywhere" my professor meant inside and outside the sphere.)
(D is...
ρHomework Statement
A sphere of radius a has a radial polarization P = krn\hat{r} where k and n are constants and n \geq 0.
a.) Find the volume and surface charge densities of bound charge.
b.) Find E outside and inside the sphere. Verify that you results for E satisfy the appropiate...
Word for word (with "hats" on the Q's)
"Problem 3.3 Show that if <h|Qh> = <Qh|h> for all functions h (in Hilber space), then <f|Qg> = <Qf|g> for all f and g (i.e., the two definitions of "hermitian" -- Equations 3.16 and 3.17 -- are equivalent). Hint: First let h=f+g, and then let h=f+ig."...
____"Again"? I've never posted a question on this site before, let alone an irrelevant one. If other people do so I don't see why that's held against me. I felt this problem was relevant to <Advanced Physics> because it comes straight from quantum mechanics homework.
____As to the...
Homework Statement
If <h|Qh> = <Qh|h> for all functions h, show that <f|Qg> = <Qf|g> for all f and g.
f,g, and h are functions of x
Q is a hermitian operator
Hints: First let h=f+g, then let h=f+ig
Homework Equations
<Q>=<Q>*
Q(f+g)= Qf+Qg
The Attempt at a Solution...