Q:

When and why do we need wave packets in quantum mechanics?

The idea of a wave packet is that you superimpose a lot of plane waves to create a localized free electron. But when and why is this useful?
It seems that wave packets are often used to derive transport equations inside solids. But in principle the true electronic wavefunctions given by Blochs theorem are perfectly valid solutions to the Schrodinger equation and are even normalizeable. So why do we ever bother to talk about wavepackets and what is the physical reason for using these?

A:

You don't "use" wave packets. They simply arise due to uncertainty.
If you have a single wave of known frequency, then it is the same everywhere.
If you combine two waves of slightly different frequency, you get a "beat" effect, due to alternate cancellation and reinforcement.
If you combine many waves of slightly different frequencies, the waves almost always cancel, but they do occasionally reinforce, but these reinforcements come further and further apart.
If you combine infinitely many waves having a distribution of frequencies, you get only one region of reinforcement, and that is called a "particle" or "wave packet".
If you are uncertain of the frequency (which you are) then you can think of it as a distribution of frequencies, and there you are.

