Hatrack River Forum: Physicists?

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Posted by Paul Goldner (Member # 1910) on :

If I have a 3 by 3 matrix,

H=V( 1 0 0
0 1 0
0 0 2), where H is the hamiltonian, and V is an energy constant, how do I find the eigenfunctions and eigenvalues for H?

Posted by Papa Moose (Member # 1992) on :

quote:
. . . how do I find the eigenfunctions and eigenvalues for H?

I'd say your best bet is to post the question at Hatrack. Someone will probably know the answer.

Posted by Paul Goldner (Member # 1910) on :

THats what I'm hoping [Smile]

Posted by fugu13 (Member # 2859) on :

Computation is pretty straightforward, this site should tell you what you need to know:

http://www.sosmath.com/diffeq/system/linear/eigenvalue/eigenvalue.html

note: having done matrix algebra myself, I find great pleasure in letting others do it [Wink]

Posted by Happy Camper (Member # 5076) on :

*twitch*

Posted by xnera (Member # 187) on :

I used to know how to do this. Man, I miss my math classes. Seriously. I loved math.

A quick google shows that most of the examples are for 2x2 matrices. Is it the 3x3 matrix that is causing a problem? If so, this Dr. Math article might be helpful.

Posted by Paul Goldner (Member # 1910) on :

Ok, calling for more help.

Does anyone know a better derivation from maxwell's equations of the speed of light then this one?

http://galileo.phys.virginia.edu/classes/109N/more_stuff/Maxwell_Eq.html

I'm pretty certain I can follow that, but if anyone wants to help out, I'd be glad of the help.

Posted by King of Men (Member # 6684) on :

It's a diagonal matrix, for God's sake. The eigenvalues are V, V, and 2V, no need for computation. If this is homework, you're in trouble.

Posted by quidscribis (Member # 5124) on :

Sheesh. I used to know how to do all that stuff. Decades ago. DO YOU HAVE ANY IDEA JUST HOW OLD YOU'RE MAKING ME FEEL?

THE NERVE OF YOU!

[/old age rant]

Whew! That was scary! [ROFL]

Posted by Paul Goldner (Member # 1910) on :

No need to be rude, KoM. It came up in one of my classes, but was never covered in that class, and I haven't taken linear algebra.