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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:


[Hx(x) + Hy(y) + Hz(z)][:lcpsi:x(x) + :lcpsi:y(y) + :lcpsi:z(z)] = (Ex + Ey + Ez)(: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:0a(2/a) (sin2((nx:pi:x)/a)dx:int:0b(2/b) (sin2((ny:pi:y)/b)dy:int:0c(2/c) (sin2((nz:pi:z)/c)dz = 1


Hope this helps a little.


Is there a website that contains all this information?




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Greg Bernhardt said in post #5 :

Kedas how can you have -10 hours logged?


That's normal, I'm a slow starter :cool:

Neg. Time: I logout first and then I login

All other people do it the other way around ;)



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

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