Eigenvalues and density of states

In summary, the conversation discusses a comparison between an analytical expression for density of states and a histogram of Hamiltonian eigenvalues. The speaker expects them to be exact copies but notices that they have different scaling and maximum values. They question if there is an error or if they are wrong to expect them to be exact copies. The units are confirmed to be the same and it is suggested to divide by the bin size to convert the histogram into units of 1/energy. The conversation ends with the understanding that the histogram is unitless and the speaker will experiment with it to see if it works.
  • #1
Niles
1,866
0
Hi guys

I have an analytical expression f(x) for my density of states, and I have plottet this. Now, I also have a complete list of my Hamiltonians eigenvalues.

When I make a histogram of these eigenvalues, I thought that I should get an exact (non-continuous) copy of my plot of f(x). They have the same form, but they are not to scale, i.e. f(x) has a maximum at ~100, while the histogram has a maximum at ~60.

Is there an error somewhere, or am I wrong to expect that they should be "exact" copies?
 
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  • #2
I am not sure whether i am correct!
some scale factor for eigenvaues or for DOS?
Also check with units of y-axis (i often get these errors when i convert meV to cm-1)
or your data is convoluted already?
 
Last edited:
  • #3
The units are the same (I have checked).

So you believe they should be the same?
 
  • #4
The units of a numerical histogram depend on the bin size chosen. Are you remembering to divide by the width of the bin?
 
  • #5
Manchot said:
The units of a numerical histogram depend on the bin size chosen. Are you remembering to divide by the width of the bin?

Isn't a histogram unit-less?
 
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  • #6
Yes, a histogram is unitless. That's why you need to divide by the bin size to get it in units of 1/energy (or 1/energy/volume, if that's what you're dealing with).
 
  • #7
I see. Thanks - I'll play around with it to see if it works. Thanks.
 

Related to Eigenvalues and density of states

1. What are eigenvalues and why are they important in physics?

Eigenvalues are a concept in linear algebra that represent the possible values of a particular system or matrix. In physics, they are important because they correspond to the allowed energy states of a physical system, such as an atom or a solid material.

2. How do eigenvalues relate to the density of states?

The density of states measures the number of energy states available in a given energy range. In quantum mechanics, the distribution of eigenvalues determines the density of states, as each eigenvalue corresponds to an energy state. A higher density of states means more eigenvalues and therefore more possible energy states.

3. What is the significance of the density of states in solid state physics?

The density of states is a fundamental concept in solid state physics, as it determines the electronic and thermal properties of materials. It is used to calculate quantities such as the electronic band structure, specific heat, and electrical conductivity of solids.

4. How are eigenvalues and the density of states used in determining material properties?

Eigenvalues and the density of states are used in various theoretical models and calculations to predict and explain material properties. For example, in the band theory of solids, the density of states is used to determine the electronic band structure and the behavior of electrons in a material.

5. Can the density of states be experimentally measured?

Yes, the density of states can be measured using various experimental techniques such as photoemission spectroscopy, tunneling spectroscopy, and scanning tunneling microscopy. These methods involve directly probing the energy states of a material and measuring their distribution, allowing for the calculation of the density of states.

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