How does parity transformation affect Bloch states?

[Joker93]

Hello!
I want to know how does a parity transformation affect Bloch states! I always knew that parity takes the position vector to minus itself (in odd number of dimensions), but I have read that it also takes the Bloch wave vector to minus itself but I have not found a satisfactory proof of this.
Thank you.

 

[Dr Transport]

Plug and chug, write out a Bloch state vector and substitute...in my head it works out pretty quickly