-blam!- this.
Edit: Okay gimme a sec.
Convert that shit to cosine.
∫[sqrt(2/L)sin(n*pi*x/L)]*[sqrt(2/L)sin(m*pi*x/L)] dx from 0 to L =
constant * ∫cos(bullshit that you can work out) - cos(bullshit but with -m)
n=/=m, therefore:
constant * integral of that shit =
constant * L * [bullshit*sin + (negative bullshit)*sin(with -m) | from 0 to L
=0
Whattuppp
English
-
I think this is something that requires more physical interpretation and can't be solved purely through mathematical manipulation.
-
I'm absolutely confidant that it can be demonstrated purely mathematically. I'll write some of it out.
-
It can't be. If n=m, it should =1.
-
Edited by HurtfulTurkey: 2/26/2014 2:28:32 AMI'm confused, you said n=/=m for this problem. Let's consolidate these replies to one thread.
-
It'll probably take more than a second.
-
Check it. (I'm not doing all that on a keyboard) Do you actually need help, or are you just trying to cause me pain?
-
I seriously need help, but I don't want to waste anyone's time. This physics homework has been a pain in the ass. It takes me hours just to figure out how to do one problem.
-
Edited by HurtfulTurkey: 2/26/2014 2:20:22 AMTo prove it just take that integral and work it out...it'll equal zero eventually. I can write it out, but I'm a bit rusty on difficult integrals and you undoubtedly know this much better than I do. I kinda of stumbled my way through eigenfunctions in differential equations.
-
It shouldn't. If it were u_n(x)^2, it would equal one. It's basically saying that the probability of a particle being in that quantum state between 0 and L is 0.
-
n =/= m , and aren't you trying to prove it does equal zero?
-
Yeah. What about your proof shows that it only equals 0 when n=/=m?
-
Well I mean there's only one solution if it's a definite integral, which it is.
-
Edited by A3LeggedBurrito: 2/26/2014 2:47:57 AMSorry, I worded that wrong. The integral is supposed to be normalized so that when n=m, it equals 1, and when n=/=m, it equals 0. The way you worked it out, it would apparently be 0 no matter what you choose for n and m. This requires some application of the Schrodinger wave function (or at least the physical interpretations behind it); it simply can't be solved by math alone. I don't want to waste anymore of your time. EDIT: Well, maybe it can be solved with math alone, but not the way you did it. Or maybe I don't fully understand what you did. Either way, thanks for trying.
-
I'm almost done. It definitely can be done.