Cooper Pairs & BCS Theory Explained

[Niles]

Hi

In my book it says that a Cooper pair is formed by a single electron state and its time-reversed counterpart. The way I have understood it, a Cooper pair is formed by the states

$$\left| {k \uparrow } \right\rangle \quad \text{and} \quad \left| { - k \downarrow } \right\rangle.$$

Where does the time-reversal come into play?Niles.

 

[element4]

Try to act with the time-reversal operator on the state $$\left| {k \uparrow } \right\rangle \quad$$ and see what you get. (You first need to look up how this operator works.)

Edit: Okay I might as well reveal that you should get $$T\left| {k \uparrow } \right\rangle \quad = \quad \left| { - k \downarrow } \right\rangle.$$

 

[Niles]

Try to act with the time-reversal operator on the state $$\left| {k \uparrow } \right\rangle \quad$$ and see what you get. (You first need to look up how this operator works.)

Edit: Okay I might as well reveal that you should get $$T\left| {k \uparrow } \right\rangle \quad = \quad \left| { - k \downarrow } \right\rangle.$$

Ahh, I see. I'll take a closer look at the operator.

Thanks.