Coulombic interaction between the proton and electron of a hydrogen atom

In summary, the position representation of the coulombic interaction between the proton and electron of a Hydrogen atom can be represented using operators. These operators would involve the principle, angular momentum, and magnetic quantum numbers. However, there are three common models for the hydrogen atom that can be used to find the equation for this interaction. The energy levels in the first model are degenerate in the magnetic moment. It would be helpful to see what you expect to see in this scenario.
  • #1
Demon117
165
1
In the position representation, its true that we can use operators to represent the coulombic interaction between the proton and electron of a Hydrogen atom. I've never actually given any thought as to what the elements of such an operator would be (in matrix form of course). I know these elements would have to do with the principle, angular momentum, and magnetic quantum numbers but I cannot seem to come up with something. Is there anyone out there that is familiar with this notion who could tell me what that would be and why?
 
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  • #2
I'm confused--are you just asking about the behavior of an electron in a Coulomb potential? If so, that's a pretty standard problem, and the equation can be found in just about any QM book. The quantum numbers you mention arise from the multiplicity of the solutions to that equation.
 
  • #3
I am confused also. There are three common models for the hydrogen atom:

1) Solution to the non-relativistic Schroedinger equation
2) Solution to the relativistic Schroedinger equation.
3) Solution to the relativistic Dirac equation (with spin-orbit coupling)

The energy levels for the first model is degenerate in the magnetic moment (no fine structure).

Why don't you show us what you expect to see.

Bob S
 

1. How does the Coulombic interaction between the proton and electron of a hydrogen atom affect its stability?

The Coulombic interaction between the proton and electron of a hydrogen atom is what holds the atom together and determines its stability. The attraction between the opposite charges of the proton and electron keeps the electron in orbit around the nucleus, creating a stable atom.

2. Can the Coulombic force between the proton and electron be broken?

The Coulombic force between the proton and electron can only be broken if an external force is applied to the atom, such as through a chemical reaction or nuclear reaction. Otherwise, the force is strong enough to keep the atom stable.

3. How does the distance between the proton and electron affect the Coulombic force?

The Coulombic force between the proton and electron is inversely proportional to the square of the distance between them. This means that as the distance increases, the force decreases and vice versa. This relationship is known as the inverse square law.

4. Does the Coulombic force between the proton and electron affect the energy levels of the hydrogen atom?

Yes, the Coulombic force between the proton and electron is responsible for the energy levels of the hydrogen atom. The closer the electron is to the nucleus, the stronger the force and the lower the energy level. As the electron moves farther from the nucleus, the force decreases and the energy level increases.

5. How does the Coulombic force change when there are multiple electrons in an atom?

The Coulombic force between the proton and electron is affected by the presence of multiple electrons in an atom. As more electrons are added, the force between the proton and each individual electron decreases due to the repulsion between the negatively charged electrons. This results in a more complex arrangement of energy levels in the atom.

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