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## 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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