High School Schrödinger Equation for the fusion of Deuterium(2H) and a Proton(H)

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The discussion revolves around finding a specific potential function V(x) for the Schrödinger equation related to the fusion of Deuterium (2H) and a Proton (H). Participants suggest that the electron can be treated as a charged particle in a spherical Coulomb potential, but the challenge lies in incorporating the strong force into the equation. It is noted that while the functional form of the proton-proton or proton-neutron interaction could theoretically be derived from quantum chromodynamics (QCD), it is not well-defined and may not be crucial for practical calculations. Instead, key focus areas include interaction cross sections and energy eigenvalues, with suggestions to use a muffin tin potential as a viable approach. Overall, the conversation emphasizes the complexity of the problem and the need for a solid understanding of both quantum mechanics and electromagnetism.
Viridun
In fact I am not sure if this is the right place to ask such a question but I'm going to ask anyways, just tell me if I am in the wrong place.
So I doing a little experiment with the Schröndinger's equation, but the problem is I can't find a certain function.
You all know the Schrödingers equation has variable for a function V(x) in the differential equation.

Now i need a specific one I need the one for the fusion of Deuterium(2H) and a Proton(H), but I can't find it anywhere.

Can anyone help me ?
 
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The electron is just a charged particle in the electric field of the proton, so you need a spherical Coulomb potential. If that's not useful for you then you may as well stop trying and instead learn about electromagnetism :)
 
Gigaz said:
The electron is just a charged particle in the electric field of the proton, so you need a spherical Coulomb potential. If that's not useful for you then you may as well stop trying and instead learn about electromagnetism :)
I know that one, and I also know how the function of that one looks, my problem is that I don't know how to get this together with the function of the strong force.
 
Ah I see, I think I read something wrong, my apologies.
The functional form of the proton-proton or proton-neutron interaction could in principle be derived from QCD if you have a really good computer. I don't think that it is known, and it is also ultimately not important. The important quantities are interaction cross sections and energy eigenvalues. Sounds funny when you do something like Quantum mechanics I at university level. But a muffin tin potential, where you have a constant very low energy around the nucleus, a wall, and a Coulomb potential outside, that approach is as good as any other.
 
Gigaz said:
Ah I see, I think I read something wrong, my apologies.
The functional form of the proton-proton or proton-neutron interaction could in principle be derived from QCD if you have a really good computer. I don't think that it is known, and it is also ultimately not important. The important quantities are interaction cross sections and energy eigenvalues. Sounds funny when you do something like Quantum mechanics I at university level. But a muffin tin potential, where you have a constant very low energy around the nucleus, a wall, and a Coulomb potential outside, that approach is as good as any other.

I probably didn't express myself to well with english not being my mother language.
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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