Issues with eigenvalues and spatial distribution of 3D hydrogen atom #9
-
Hi, But when I ran the script
The ground state should be -13.6eV, but the script returned -8.26297717eV. Also, I found the grid is 303030 with the actual length of each edge are also 30A30A30A. Should I make a finner grid to solve for a better result?
Though I came with such issues, I must say thank you for giving a feasible numeric approach to solve the 3D single particle schrodinger equation and giving fancy results to help students understanding the QM. Looking forward to your reply! |
Beta Was this translation helpful? Give feedback.
Replies: 1 comment 12 replies
-
The problem is the spatial discretization, as you said 30x30x30 is very small, especially considering that the Coulomb potential has a singularity. The problem is fixed using a smoother discretization, but If you try a discretization smoother than (50x50x50) you will soon find that a personal computer cannot handle it. But I already fixed the problem! It happens that LOBPCG algorithm can deal with very large grids (200x200x200) and improve the accuracy of the solver considerably. I'm working on implementing it. I will update the repository with the implementation this weekend. Using a 200x200x200 grid these are energies:
while the analytical ones are:
This is the best you will be able to get with a 3D simulation. ( the computation last about 100 seconds on a good pc) But the hydrogen atom has a clearly azimuthal symmetry and the problem can be reduced to 2D.
|
Beta Was this translation helpful? Give feedback.
The problem is the spatial discretization, as you said 30x30x30 is very small, especially considering that the Coulomb potential has a singularity. The problem is fixed using a smoother discretization, but If you try a discretization smoother than (50x50x50) you will soon find that a personal computer cannot handle it.
But I already fixed the problem!
It happens that LOBPCG algorithm can deal with very large grids (200x200x200) and improve the accuracy of the solver considerably. I'm working on implementing it. I will update the repository with the implementation this weekend.
Using a 200x200x200 grid these are energies:
[-13.52, -3.384, -1.502, -0.826, -0.531] eV
while the analytical one…