Question

please describe it.....

Answer 1

Bloch's theorem tells you how an electronic wavefunction would look like when subjected to a periodic potential.

In solid state physics, the most elementary theory of conductivity was the free electron theory which supposed that electrons were free to move inside the lattice in a constant potential (which may as well be taken to be zero) in a manner analogous to molecules in an ideal gas.

However, later it was realized that the oversimplified assumption that the potential in which the electrons move is zero is not quite the actual picture: Electrons move in the periodic potential of the positive ions. The periodicity arises due to the periodic arrangement of positive ions in the lattice.

Then solving the Schrödinger equation for such a periodic potential becomes the task which is quite difficult. Here, Bloch's theorem comes to the rescue. It tells us that the wavefunction is the free particle wavefunction modulated by a function of the same periodicity as that of the potential. Such functions are the so called Bloch functions.

This way the Bloch's theorem tells us the general form of the wavefunction for such a Bloch Wave. All one has to do is to substitute it into the Schrödinger equation with suitable boundary conditions and find the form of the Bloch function.