Just to check Schrodinger equation with 2 electrons

[jonjacson]

Hi folks,

I just want to check I understand correctly the Schrödinger equation for two electrons.

https://en.wikipedia.org/wiki/Schrödinger_equation#Time-independent_equation

With control F you can find "two electrons atoms or ions" section.

Let's assume the wave function = x₁ ²+ x₂² and let's test if it satisfies the differential equation. (Instead of position vector r y use only x in 1D and the Laplacian operator is just a derivative respect x):

E * (x₁² + x₂²) = -h² * (2/μ) + e²/4piε₀ * (1/x₂-x₁ - Z ( 1/x₁+1/x₂)) * (x₁² + x₂²)

In case this equation were true I would have found a solution, Is this correct?

 

[ZapperZ]

This is very odd.

In 1D, you do not get that type of a central potential. You have to solve this in 3D if you want to keep that potential.

Zz.

 

[jonjacson]

This is very odd.

In 1D, you do not get that type of a central potential. You have to solve this in 3D if you want to keep that potential.

Zz.

This demonstrates opening this thread was a good idea.

Do you know any book or thread were the 2 body problem is approached. Since I read it is not solvable I assume nobody is publishing failed attempts. I suppose mathematicians have tried very hard to solve this equation and maybe they don't know how to do it, but for sure they know a lot of ways not to solve it right?

Where could I learn about this?