When do we use notion of effective mass

[amitrt]

If effective mass in schrodinger 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 schrodinger 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

 

[denian]

The notion of effective mass is used in a variety of situations in physics, particularly in the study of semiconductors and solid state materials. In general, the effective mass is a concept that allows us to simplify complex systems and make them more tractable for analysis.

In the context of the Schrodinger equation, the effective mass is used to account for the coupling between different bands or energy levels in a solid state material. This is particularly important in the study of electronic properties in semiconductors, where the behavior of electrons is strongly influenced by the presence of other electrons and the lattice structure of the material.

By using the effective mass, we are able to simplify the problem by treating the electron as if it were moving in a uniform medium, rather than taking into account the effects of other electrons and the complex lattice potential. This allows us to make more accurate predictions about the behavior of the electron and its interactions with the material.

Overall, the notion of effective mass is a powerful tool in the study of solid state materials and allows us to better understand the behavior of electrons in these systems. It is an important concept for scientists and engineers working in fields such as semiconductor technology, materials science, and condensed matter physics.