Bcs theroy, just an easy algebraic manipulation

[Derivator]

bcs theroy, just an "easy" algebraic manipulation

Hi folks,

i'm sitting here for hous and I'm wondering, how one can find formula 3.35' on page 61 in Tinkham's book: http://books.google.de/books?id=k6A...superconductivity&pg=PA61#v=onepage&q&f=false

I think, it should be possible to find this formula just with some algebraic manipulation of

|u|^2 + |v|^2 = 1
and
|v/u| = (E - xi)/|Delta|

However, I can't see how... I'm getting nuts...

--
derivator

 

[gabbagabbahey]

I think, it should be possible to find this formula just with some algebraic manipulation of

|u|^2 + |v|^2 = 1
and
|v/u| = (E - xi)/|Delta|

It is possible, but it's much easier to do as the author suggested and use (3.29c) together wuith the normalization condition:

[tex]u^2+v^2=1[/itex]
$$v^2-u^2=-\frac{\xi}{E}$$

...add the two equations together, divide by 2 and you get $v^2$
...subtract the 2nd from the 1st and divide by 2 and you get $u^2$

 

[Derivator]

Thank you!