- #1
g.lemaitre
- 267
- 2
Homework Statement
I'm a little weary of posting this in this forum. If I post it in the math section it will be answered in about 30 min whereas here it might take about 5 hours, but we'll see.
Homework Equations
The Attempt at a Solution
Number one, I'm not exactly sure how they get from
[tex]\int \phi_1^* (c_1\phi_1 + c_2\phi_2)d\tau = c_1 + c_2 d [/tex]
I think it's because
[tex] \phi^*\phi = 1[/tex] but I'm not sure.
Number two, I don't understand the following step:
[tex] \int (c_1\phi_1 + c_2 phi_2)*(c_1 \phi_1 + c_2\phi_2)d\tau = c_1^2 + c_2^2 + 2dc_1c_2 [/tex]
why does [itex]\phi[/itex] disappear?
I figure that it must have something to do with the fact that [itex]\phi_1[/itex] is orthogonal which means it = 0
Number three, I can't get step 3. I put the equations as follows:
[tex]
c_1 + c_2d = 0
c_1^2 + c_2^2 + 2 dc_1c_2 = 1
c_1 = -c_2d[/tex]
therefore
[tex]
(-c_2d)^2 + c_2^2 + 2d(-c_2d)c_2 = 1
(-c_2d)^2 + c_2^2 - 2(c_2d)^2 = 1
[/tex]
And then I can go no further.
Number four, I don't understand how
[tex]
\int (\phi_1 + \phi_2)*(c_1\phi_1 + c_2\phi_2)d\tau [/tex]
simplifies to
[tex]
(c_1 + c_2)(1+d)
[/tex]
Number five, what do they mean by 2 and 5 gives
[tex]
\frac{(\phi_1 - \phi_2)}{\sqrt{2-2d)}}
[/tex]
As you can see I'm real clueless with regards to this stuff. I've got a private tutor lined up but I won't be able to meet with him until sometime next week.
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