That's why I wrote 'modulo rotations and translations', I consider two positional configurations equivalent if they can be translated and rotated into each other.
Edit: I should perhaps clarify that there is some means of controlling the forces between the particles, i.e. the particles can be...
If we have N unique point masses, is it possible to use only internal forces (i.e. forces between each pair of masses) to reach any configuration of the points (modulo rotations and translations)?
I assume this is well known, but don't know where to find a proof. Perhaps by induction from N=2...
Yes, this can happen in general but I have never heard of this effect at mirror surface. In bulk material the process is called four wave mixing, this page has good overview: http://www.rp-photonics.com/four_wave_mixing.html . At the atomic scale you have to take many different things into...
"Doubly occupied" orbitals have no net angular momentum, because the two spinors of each pair are related by time reversal. Their angular momenta therefore exactly cancel out. Some textbooks gloss over this fact and just show you that the two spins are anti-parallel, but it's also true for the...
Hi,
I wonder if there is some agreed-upon best way to reconstruct the matrix of a positive definite operator A using "sampling" (like in tomography). More in detail I want to do this:
I have many small sets of basis functions. The sets are in general not orthogonal. I compute matrix elements...
Hi all,
I have a problem related to quantum mechanical description of vibrational motion in molecules. I would like, for efficiency, to integrate over symmetries (global rotations) of the molecule.
I would like to prove (or disprove) that all points in R^N can be reached by rotations from a...