When do we use notion of effective mass

[amitrt]

If effective mass in Schrödinger equation takes into account for coupling by other bands or so to say by other electrons, and in this way we don't care about effect of other electrons and deal with lattice potential.

 

[marlon]

If effective mass in Schrödinger equation takes into account for coupling by other bands or so to say by other electrons, and in this way we don't care about effect of other electrons and deal with lattice potential.

What exactly is the question here ?

Intuitively, effective mass is a concept that uncouples one many body problem into a set of one body problems that are more easu to solve (i mean, of which the Schrödinger equation, ie the SE, is easier to solve).

Suppose you have 100 electrons mutually interacting through a coulombic potential. The SE cannot be solved exactly because of the mutual coupling between all the electrons (electron 1 interacts with electron 2,3, etc). To uncouple this many body system, we convert it into a system where you have "new electrons" interacting in a background potential. So, you look at the problem as if the new electrons are no longer interacting with each other but with some background potential. Since both systems need to be equivalent (ie you need to describe the same physical reality) you need to compare both systems : the original system as mutually interacting electrons, the new system has non interacting electrons in a certain potential well. To make sure that both systems are equivalent, we change the mass of the electrons in the second system, in such a way that both SE are describing the same reality. This new mass is the effective mass, which can be defined as the electron mass + some interactions (ie energy of those interactions) to uncouple the many body problem into many one body problems.

That is the philosophy behind effective mass.

marlon