Electron - Phonon scattering, deriving the contribution to

[rwooduk]

... electron transport.

1. Homework Statement
Electron - Phonon scattering, derive the contribution to electron transport.

Homework Equations

Trig.

The Attempt at a Solution

Am I being REALLY stupid here, I can't see how the equation matches the triangle.

If you resolve K_F^' doesn't K_F^' cos theta= K_F

The only thing I can think is that it's an approximation and delta K_F is very small?
Thanks for any help

 

[SammyS]

... electron transport.

1. Homework Statement
Electron - Phonon scattering, derive the contribution to electron transport.

Homework Equations

Trig.

The Attempt at a Solution

Am I being REALLY stupid here, I can't see how the equation matches the triangle.

If you resolve K_F^' doesn't K_F^' cos theta= K_F

The only thing I can think is that it's an approximation and delta K_F is very small?
Thanks for any help

Yes, I think you're right about ΔK_F needing to be small. Also, I think φ needs to be small enough so that cos(φ) ≈ 1 , while (1 - cos(φ) ) can't be ignored.

It looks to me like ΔK_F is just a difference in magnitudes of the vectors and not the magnitude of the vector difference.

 

[rwooduk]

Yes, I think you're right about ΔK_F needing to be small. Also, I think φ needs to be small enough so that cos(φ) ≈ 1 , while (1 - cos(φ) ) can't be ignored.

It looks to me like ΔK_F is just a difference in magnitudes of the vectors and not the magnitude of the vector difference.

Thanks very muvh for the reply.