Thomas-Fermi Screening Approximation

• calvinjhfeng
In summary, the conversation discusses confusion about the math in Thomas-Fermi's approximation and the difference between approximating a length and energy. The professor explains that the approximation is used to find the length at which normal conductors screen electric field. The person asking the question is looking for a brief explanation of the Thomas-Fermi method and will go to the library to consult a book.
calvinjhfeng
I got quite confused with the math in Thomas-Fermi's approximation.
I thought it was supposed to approximate a length but the math from a textbook gives energy instead.
I don't understand what is it trying to approximate.

My professor told me that normal conductors screen electric field at a very short distance ≈1 Angstrom. He said that is the Thomas-Fermi approximated length.

How to derive that length?

calvinjhfeng said:
I thought it was supposed to approximate a length but the math from a textbook gives energy instead.

And what do you suppose us to do now? Trying to guess what might actually be written in your unspecified textbook?

DrDu said:
And what do you suppose us to do now? Trying to guess what might actually be written in your unspecified textbook?

I supposed a brief explanation of Thomas-Fermi method on approximating this screening length so i at least have an idea of what is going on.
However, I agree that I should have been more specific with the questions. Please allow me to go to library again and pull out the book again.
Also thank you for trying to help.

deleted

calvinjhfeng said:
I supposed a brief explanation of Thomas-Fermi method on approximating this screening length so i at least have an idea of what is going on.
However, I agree that I should have been more specific with the questions. Please allow me to go to library again and pull out the book again.
Also thank you for trying to help.

which book did you consider in the end?

1. What is the Thomas-Fermi Screening Approximation?

The Thomas-Fermi Screening Approximation is a theoretical model used in condensed matter physics to describe the behavior of electrons in a solid. It is based on the Thomas-Fermi model, which assumes that the electron density is constant throughout the solid and that the electrons move independently of each other.

2. How does the Thomas-Fermi Screening Approximation work?

The Thomas-Fermi Screening Approximation works by taking into account the effects of the surrounding electrons on the movement of each individual electron. It does this by introducing a screening potential that accounts for the repulsive forces between electrons, which allows for a more accurate description of how the electrons move in a solid.

3. What are the limitations of the Thomas-Fermi Screening Approximation?

One of the main limitations of the Thomas-Fermi Screening Approximation is that it does not take into account the quantum nature of electrons. This means that it is not accurate for describing systems with low electron densities or in situations where quantum effects are important. Additionally, it does not take into account the effects of electron-electron interactions beyond the mean-field level.

4. What are the applications of the Thomas-Fermi Screening Approximation?

The Thomas-Fermi Screening Approximation is commonly used in theoretical studies of condensed matter systems, such as metals and semiconductors. It is also used in the study of plasmas and in nuclear physics. Additionally, it has applications in the design of electronic devices and in the calculation of material properties.

5. How does the Thomas-Fermi Screening Approximation differ from other theoretical models?

The Thomas-Fermi Screening Approximation differs from other theoretical models, such as the Hartree-Fock method, in that it is a simpler and more computationally efficient approach. It also takes into account the effects of electron screening, which is not considered in other models. However, it is less accurate than more sophisticated models that take into account quantum effects and electron-electron interactions beyond the mean-field level.

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