Math Symbols

[Tom Mattson]

Could someone please show me how to do stuff like this:

 

Originally posted by fafalone

I banned myself last night. After blike unbanned me this morning, I removed the limit on number of images per post, so let's try this again. I gave background equations for visualization in 2D first, but I'm skipping that. This isn't nearly in depth, but still has my basic idea. Also realize that I'm a freshman who has self-taught himself everything he knows about QM

 

Begin by using the 3D Hamiltonian operator in the Shrodinger equation:

 

[-h²/2m (:pdif:²/:pdif:x² + :pdif:²/:pdif:y² + :pdif:²/:pdif:z²) + V(x,y,z)]:lcpsi:(x,y,z) = E:lcpsi:(x,y,z)

 

H(x,y,z):lcpsi:(x,y,z) = E:lcpsi:(x,y,z)

 

Now use separation of variables:

 

[H_x(x) + H_y(y) + H_z(z)][:lcpsi:_x(x) + :lcpsi:_y(y) + :lcpsi:_z(z)] = (E_x + E_y + E_z)(:lcpsi:_x(x) + :lcpsi:_y(y) + :lcpsi:_z(z))

 

From this, you should be able to see how working with the wave function in 3 dimensions is just like in 2... you're basically solving the same equation 3 times. Normalization gives:

 

:int::int::int:|:lcpsi:(x,y,z)|²dxdydz = :int:₀^a(2/a) (sin²((n_x:pi:x)/a)dx:int:₀^b(2/b) (sin²((n_y:pi:y)/b)dy:int:₀^c(2/c) (sin²((n_z:pi:z)/c)dz = 1

 

Hope this helps a little.

 

Is there a website that contains all this information?

 

Thanks,

Tom

[fafalone]

How to use the symbols or how to do the problems?

 

I just found a site with gifs of the symbols and uploaded as custom smilies.

[Tom Mattson]

:slaphead:

 

Clicking on "get more" sure helps.

 

Thanks,

Tom

[Kedas]

test

[dethfire]

Kedas how can you have -10 hours logged?

[Sayonara]

lol

 

Server probs the other day.

[Dudde]

no fingers pointed at blike of course

[Kedas]

Greg Bernhardt said in post #5 :

Kedas how can you have -10 hours logged?

 

That's normal, I'm a slow starter

Neg. Time: I logout first and then I login

All other people do it the other way around

 

serious:

I logged in while traveling at almost light speed and that messed up the time on the server, I wont do it agian, sorry.

[Dudde]

he's gettin' there