Photon absorption and probability of atomic electron transition

In summary, The Schrodinger equation can be used to solve for allowed energy levels and wavefunctions of the hydrogen atom. When a photon is absorbed, the atom's energy increases and the electron moves to a higher energy level. However, the process of absorption is more complex and involves calculating the probability of transition using the wavefunctions of the orbitals involved. This can be done using the Fermi's Golden Rule and a working knowledge of quantum mechanics and quantum optics. A recommended resource for further understanding is Cohen-Tannoudji's book on atom-photon interactions. The interaction term is first omitted in the Schrodinger equation to determine non-perturbed wavefunctions, and then the interaction is taken into account perturbatively using the dip
  • #1
PhysicsAm55
2
0
I have only taken one very intro quantum mechanics class and the furthest we got was solving the Schrodinger equation for the Coulumb potential of the hydrogen atom.
So we solved for the allowed energy levels and the wavefunction for the hydrogen atom. We also learned how using the wavefunction, the electron orbitals can be constructed as probability "clouds" around the nucleus.

Now the question I have is how does one deal with this hydrogen atom absorbing a photon in terms of the Schrodinger equation?

I was taught in modern physics that when an atom absorbs a photon, its energy is increased and the electron moves up to a higher energy level. But is it even correct to say that the atom absorbs the photon? I know some sources state and my professor stated a few times that the photon 'bumps' the electron up to a higher energy level but I assumed that this was a simplified and wrong way to look at the situation since it is treated like a classical collision (the photon actually colliding with the electron). I just wanted to mention this and ask here if I was right to dismiss this classical picture of the situation?

To try to answer my own question: I guess when the photon comes close enough to the hydrogen atom you must resolve the Schrodinger equation with a different potential energy function. This is different from anything I have learned because the potential would now depend on time so I would not know where to begin here, but let's say you solved the Schrodinger equation and find the wavefunction. Do you use this wavefunction to compute the probability of the photon being absorbed? and for the electron making an atomic transition? If so how would you go about this? Lastly how would you find the probability of Auger electrons after the excited electron returns to its ground state.

I thank you for your time and eagerly await your response!
 
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  • #2
Does anyone have any recommended resources that could answer my questions?
 
  • #3
There is no simple answer to your question.
Yes, it is possible to calculate all those things, and yes the probability amplitude for a transition depends on the overlap of the wavefunctions of the orbitals involved in the transitions.
Look up e.g. Fermi's Golden Rule.

However, the details are quite complicated and require both a working knowledge of "standard" QM at the level of e.g. Sakurai, and some knowledge about quantum optics.
The best reference I can think of is Cohen-Tannoudji's book on atom-photon interactions.
 
  • #4
The electron-photon interaction term (always present in nature) is first omitted in the Schroedinger equation. This gives the atomic wave functions (non perturbed). Then the interaction term is taken into account perturbatively. Often one uses the so called dipole approximation, so the matrix elements contain simply r instead of exact interaction potential.
 

1. What is photon absorption and how does it relate to atomic electron transitions?

Photon absorption is the process in which an atom absorbs a photon of energy, causing an electron to transition to a higher energy level. This transition can occur when the energy of the photon matches the energy difference between two atomic energy levels.

2. How does the probability of an atomic electron transition change with different photon energies?

The probability of an atomic electron transition increases with higher photon energies. This is because higher energy photons have a greater chance of matching the energy difference between two atomic energy levels, allowing for a higher probability of absorption.

3. What factors influence the probability of an atomic electron transition?

The probability of an atomic electron transition is influenced by the energy of the photon, the energy difference between atomic energy levels, and the properties of the atom itself, such as its electron configuration and atomic structure.

4. Can the probability of an atomic electron transition be predicted or controlled?

The probability of an atomic electron transition can be predicted using mathematical models and quantum mechanics. However, controlling this probability is more difficult and requires precise manipulation of the energy of the photon and the atomic environment.

5. What are some practical applications of understanding photon absorption and atomic electron transitions?

Understanding photon absorption and atomic electron transitions is important in fields such as spectroscopy, laser technology, and materials science. It allows scientists to study the properties of atoms and molecules, and to create precise and efficient energy sources and technologies.

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