Explaining Electron Emission and Photon Interactions in Quantum Mechanics

In summary, in introductory quantum mechanics, we assume that the Hamiltonian of the hydrogen atom does not change with time, making the solution of the Schrödinger's equation easier to obtain. This means we do not seek to explain electron emission or transitions in orbit. There is a mathematical model, known as time dependent perturbation theory, that explains what happens to the electron when it is "hit by a photon" or when the atom emits a photon and returns to the ground state. This is similar to the concept of EM wave emission in classical mechanics. For more information, you can refer to the link provided.
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From my understanding, when solving the hydrogen atom (getting the wavefunction of the electron) in introductory quantum mechanics, we assume that the Hamiltonian doesn't change with time (because in this case the solution of the S. equation is separable and therefore "easy" to obtain). In other words, we assume that the system proton+electron is stable so that we dismiss any emission of the electron. It means we do not seek to explain using the Schrödinger's equation how an electron emits and do its transition of "orbit".
I would to know if there is some mathematical model that exactly explain what happens to the electron when it get "hit by a photon" or when the atom is in excited unstable state and then emits a photon and comes back to the ground state.

When a charge is accelerated it must emit EM waves according to classical mechanics. Is there a similar description in quantum mechanics? If so, where can I read more about this?
 
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Thank you very much.
 

1. What is an electron emitting a photon?

An electron emitting a photon refers to the process in which an electron releases a tiny packet of energy, called a photon, as it moves from a higher energy state to a lower energy state.

2. How does an electron emit a photon?

Electrons emit photons through the process of spontaneous emission, which occurs when an electron in an excited state spontaneously drops to a lower energy state and releases a photon.

3. What is the relationship between an electron and a photon?

An electron and a photon are both fundamental particles of matter and energy, respectively. Electrons carry a negative charge and are found in the outer shells of atoms, while photons are massless particles of light and carry energy in the form of electromagnetic radiation.

4. Why is the emission of a photon by an electron important?

The emission of photons by electrons is important because it plays a crucial role in countless natural processes, such as photosynthesis, vision, and energy generation in stars. It also has practical applications in technologies such as lasers and LEDs.

5. Can an electron emit multiple photons?

Yes, an electron can emit multiple photons in a process called stimulated emission. This occurs when a photon interacts with an excited electron, causing it to release a second photon with the same energy, frequency, and direction as the first. This process is the basis for the amplification of light in lasers.

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