What is the difference between local density of states and density of state?

[snooper007]

what is the essentail difference between local density of states and density of state?

It is very difficult to figure it out

 

[Gokul43201]

In a non-homogeneous material, there is no reason for the DOS to be spatially invariant. For instance, in a finite crystal, it is unwise to expect the DOS in the bulk to equal the DOS at the surface. So, instead of a macroscopically averaged density, n(E), we use a spatially dependent density n(E,x,y,z).

The LDOS is typically probed by an STM, where the tunnel current is a function of the LDOS just beneath the tip.

See also, Michael Marder, "Condensed Matter Physics", Ch. 8

 

[snooper007]

Thank you Gokul43201!