Recent content by Fetchimus

Thank you so much! I got the first part of your expression! Was not able to simplify it down to the second part though where you have cos(3ωt+π/4).

I have let θ= (E1-E2/ħ)t

Okay I think I see what you're saying. So for the RE term I have [(1-i)/2]√2/2(cosθ+isinθ)<x>12 = [(√2/2L)cosθ+(√2/2L)sinθ](2/L)(-8/9(L/π)2) which simplifies to 2RE = [√2cosθ+√2sinθ](-16L/9π2) So <x> = (1/2)L + 2RE

Are you saying that, <x>12+<x>21 = <x>12 + <x>12* and that's where my sum of a complex # and it's conjugate is coming from? I totally forgot about that formula tbh. Thanks for the reminder. I'm having trouble getting the real part out. I feel as though the exp term goes away by default due to...

Definitely need to take some time to let that sink in. So for part e) I have <x> = (1/2)L - (4L/9π2)(√2)[(1-i)ei(E1-E2)t/ħ+(1+i)ei(E2-E1)t/ħ]. If this is correct I'll be on my way. If you have something different I can simply go back and check my math at this point.

There is also a part f) where I am asked to find <p>, but seeing as how I could simply use m(d/dt)<x> I was really just hoping to get the proper answer for <x>. I have math worked out for everything, but the typing would take forever, lol. Btw, thanks for all your help so far. It is much...

For part c) I got (5/2)(π2ħ2/2mL2) For part d) I got (1/2) Spent a few hours on these because I was uneasy about not seeing t anywhere in my answer, but a buddy of mine that has done this problem before claims that these are correct. Perhaps they are not. Not entirely sure.

Okay. So doing integration by parts on the integral and once again ignoring the constants for the time being, I ended up with -(L/π)2+(L/3π)2. Is this the correct result when evaluating the integral from 0 to L?

I believe it's ei(E1-E2)t/ħ. I left it out for the sake of pinpointing the integral itself.

Homework Statement A particle of mass m, is in an infinite square well of width L, V(x)=0 for 0<x<L, and V(x)=∞, elsewhere. At time t=0,Ψ(x,0) = C[((1+i)/2)*√(2/L)*sin(πx/L) + (1/√L)*sin(2πx/L) in, 0<x<L a) Find C b) Find Ψ(x,t) c) Find <E> as a function of t. d) Find the probability as a...