Greg von Winckel
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 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