## Wednesday, July 11, 2012

### Sunyaev-Zel'dovich effect

the thermal Sunyaev-Zel'dovich effect is usuall derived for Compton-interactions of the CMB photons with a thermal gas of electrons - is the assumption of thermality necessary?

bonus: what's happening if the electrons become relativistic?

extra bonus: can you express $i^{+i}\pm i^{-i}$ in terms of trigonometric functions?

#### 1 comment:

1. using results from previous CQW bonus questions such as $i^{+i} = \exp(-\pi/2)$ and $i^{-i} = \exp(+\pi/2)$ as well as the relations $\cosh(i\phi) = \cos(\phi)$ and $\sinh(i\phi) = i\sin(\phi)$ from the Euler-relation and the definitions of the hyperbolic functions gives $i^{+i}+i^{-i} = 2\cosh(i^2\pi/2) = 2\cos(i\pi/2)$ and $i^{+i}-i^{-i} = 2\sinh(i^2\pi/2)=2i\sin(i\pi/2)$.