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seen Jul 4 '11 at 14:36

Jun
30
answered Fermionic interaction potentials
Jun
29
comment Fermionic interaction potentials
I have indeed tried a Lorenzian potential and observed spectral convergence. My hope, however, was not to try an arbitrary smooth potential, but one that is used in practice to model something. Some analytically solvable 1D fermionic systems would be of interest anyway. Do you have a reference for any of those?
Jun
28
comment Fermionic interaction potentials
I have written a spectral code for computing eigenstates of 1D fermion systems with arbitrary confinement and interaction potentials. I am looking for model problems to test the code on and have already tried solving the (no spin) $n$-particle problem $$\left\{-\frac{\hbar^2}{2m}\nabla^2 + \sum\limits_{j=1}^n V_{ext}(x_j) + \sum\limits_{k=j+1}^n V_{int}(x_j-x_k)\right\}\psi(\mathbf{x})=E\psi(\mathbf{x})$$. When I use Coulomb interaction for $V_{int}$, the method converges quadratically. I am looking for problems with smooth $V_{int}$ to see if the convergence improves.
Jun
27
awarded  Student
Jun
27
awarded  Editor
Jun
27
revised Fermionic interaction potentials
added 486 characters in body
Jun
27
comment Fermionic interaction potentials
Yes. Ideally, $V(r_1-r_2)$ is $C^\infty$. At the very least is there any such model for fermionic particles where $V(r_1-r_2)$ is continuous at $r_1=r_2$?
Jun
27
asked Fermionic interaction potentials