Relation between crystal momentum of the electron and other momentums

[hokhani]

As far as I know, $$F_ {ext} = d (\hbar k)/dt = d p_{electron} / dt + d P_{crystal} /dt.$$ could one say that $$\hbar k = P_{electron} + P_{crystal}?$$

 

[DrDu]

Crystal momentum is an interesting phenomenon.
Maybe you want to read my post #15 in the following thread:
https://www.physicsforums.com/showthread.php?t=611109
I have never seen this discussed in solid state literature.