Sketch the functions dependance on energy

[greeniq]

Hi guys,
I just started a course which is called quantum nanodevices and i need help in one of the exercises,
ex. calculate, using periodic boundary conditions for free particles in a box, the quantity

Q(ε)=(1/V) Σp δ(ε- εp)

in the large system limit, 1)in three dimensions,2)in two dimensions, 3) in one dimension. 4)and sketch the functions dependence on energy. 5) what is the physical meaninig of the quantity?

please guys i need your hints about this ex. and I need to know where can i find related articles about this subject.

thanx so much in advance.
IQ

 

[Cthugha]

Have a look at your function. What does it do?
You sum over all possible values of p (which means in fact summing over all possible combinations of the k-vector) and add 1 whenever there is a state with the sought energy at this certain combination of k-vector entrys. This is the sum of states of a given Energy value. Divided by the volume you get the density of states, which is your quantity Q.

So what you want is the density of states for bulk material (3D), quantum wells (2D), quantum wires (1D) and quantum dots (0D).
As this seems to be a homework question I don't want to give you every detail.
However, if you are really frustrated, looking http://britneyspears.ac/physics/dos/dos.htm" might help.

 

[greeniq]

Thanx Cthugha
this is a homework, I appreciate your replay, I will read this article, and maybe I will need some explanation, because I am new into quantum physics.
Thanx again