Yes, right, I'll fix that. The minus sign came from me knowing it appears in the end but it's not correct there.
EDIT: apparently I can't edit the first post in the thread? Sorry for that.
In regular notation,
$$P_i = \sum_j P_{ij} $$
I suppose I could get the same result by multiplying by an array of ones with a single index, I just don't know if there's a conventional symbol for that.
Homework Statement
I'm dealing with some pretty complex derivatives of a kernel function; long story short, there's a lot of summations going on, so I'm trying to write it down using the Einstein notation, for shortness and hopefully reduction of errors (also for the sake of a paper in which I...
Tried that, they're pretty consistent. Though one thing that messes with the results is if I start the grid too close to zero (zero itself is, of course, excluded, as it would make the potential diverge). I suppose numerical precision screws it up.
To clarify, I'm writing only the radial equation because I'm interested only in the radial density part of the solution (since I need it to compute the expectation value of a quantity that we assume has spherical symmetry too), but the potential is spherical. Therefore the usual logic with ##l##...
Ok, so I think I figured this out. I tried my code on the hydrogen atom problem and managed to map the functions to the known orbitals, so that clarifies things a bit. Pic incoming:
So what's happening here is we have eigenvectors for the 5 lowest energy solutions I found plus eigenvalues for...
Ok, but in the hydrogenic atom solution, ##n## is a parameter. However in this case there's no obvious ##n##. There's ##l##, appearing in the centrifugal term of the modified potential ##V_{rot}##. Now when I solve for that I get a number of eigenstates (ideally infinite ones, in practice as...
Yeah, this. If you had to recover the full wavefunction I'd have to compute ##R(r) = \chi(r)/r##, but the problem with that is that the precision goes to hell for small values of ##r##. However I only need to compute the expectation value of a radial quantity, which means I don't need to do that...
Thanks! This is the key point for me. You mean you think I should only take the first eigenstate for ##l=0##, the first two for ##l=1## and so on? Do you know how can I test for the validity of this or if there is somewhere I can consult as a reference? About the solution existing, I believe...
Ah, no, he suggests Gaussian but for what I know that's simply a molecular DFT package. I know many of those but they aren't generic solvers, they solve chemical systems, using specific potentials representing atoms. Plus they work with a 3D grid, which... I could do I guess, it's just that...
Good question, I don't know. I was wondering exactly about whether something like this was happening and if so how can it be dealt with numerically without any assumptions on ##V(r)##.
Hi all, I'm trying to compute the solutions to a general case for a Schroedinger equation with a radial potential but I'm stuck on a rather small detail that I'm not sure about. It's well known that I can perform the change of variables to spherical coordinates and express the radial part of the...
Sorry for jumping in without having read the full 22-pages thread but just excerpts of it, but this is a topic I'm dearly interested in as I find Bohmian mechanics pretty fascinating, if only because it provides a very useful way to visualise otherwise pretty alien concepts. The paper linked...
There actually was a similar experiment just a few weeks ago in which they crowdsourced random choices to internet users all around the world. I don't know if the outcomes have been announced yet though.