Photoemission from a non-interacting electron gas

In summary, when dealing with the Hamiltonian in operator or second quantization notation, it is necessary to include the potential energy and external forces, as well as annihilation and creation operators for the particles involved. When treating the surface of a crystal, it is important to consider the electrostatic and electromagnetic properties of the surface, the refractive index of the material, and the surface roughness.
  • #1
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Homework Statement
Calculate the intensity of photoelectrons escaping a semi-infinite metallic crystal as a function of energy and momentum in the dipole approximation.
Follow these steps:
. Write down the corresponding Hamiltonian in the operator notation and in the second-quantization notation.
. Discuss the possible ways of treating the surface of the crystal.
. Derive the expression for the photocurrent in the three-step model.
. What approximations were necessary to arrive at this expression, and when might they break down?
Relevant Equations
H=?
I had another excercise of the long list of the same topic (solid state physic) where I need a bit of help. All other excercise where about interband transition, dispersion relation, refracting and absorption coefficient, x-rays and so on, and I managed to solve them or I think I will be able to do so, for this one I have a lot of questions:

-The Hamiltonian on the operator notation should be just the hamiltonian of a dipole?
-The Hamiltonian with the second quantization notation should have an anhilation operator for the photon and the electron or should have also a creation operator for the ejected electron?
-I have no idea on how to treat the surface of the crystal :headbang:

I'm still blocked at the first three points, but if you have suggestion about the other two (or how to search for explanation about them) every help it's welcome :smile:
 
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  • #2
The Hamiltonian on the operator notation should be just the hamiltonian of a dipole. This would include the potential energy of the dipole and any external forces acting on it. The Hamiltonian with the second quantization notation should include an annihilation operator for the photon and the electron, as well as a creation operator for the ejected electron.To treat the surface of the crystal, you need to consider the boundary conditions at the surface. This includes the electrostatic and electromagnetic properties of the surface, such as the surface charges and currents, and how they interact with the incident wave. You also need to consider the refractive index of the material, which determines how much of the wave is reflected and transmitted. Finally, you need to consider the surface roughness, which affects the scattering of the wave.
 

1. What is photoemission from a non-interacting electron gas?

Photoemission from a non-interacting electron gas is a physical phenomenon in which electrons are emitted from a solid material when it is exposed to light. This process is also known as the photoelectric effect.

2. How does photoemission from a non-interacting electron gas occur?

When a photon of sufficient energy strikes the surface of a solid material, it can transfer its energy to an electron, causing it to be ejected from the material. This process is known as photoemission and is typically seen in materials with low work functions, such as metals.

3. What is the significance of studying photoemission from a non-interacting electron gas?

Studying photoemission from a non-interacting electron gas can provide valuable insights into the properties of materials, such as their electronic structure and surface characteristics. It is also an important tool for studying the interaction of light with matter.

4. What are some applications of photoemission from a non-interacting electron gas?

Photoemission from a non-interacting electron gas has many practical applications, including solar panels, photocells, and photodiodes. It is also used in scientific research to study the properties of materials and to develop new technologies.

5. Are there any limitations to using photoemission from a non-interacting electron gas?

One limitation of photoemission from a non-interacting electron gas is that it can only provide information about the surface of a material, as the emitted electrons come from a shallow depth. Additionally, the process is highly dependent on the energy of the incident light and the properties of the material, making it difficult to control and reproduce in experiments.

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