Real electron charge clouds in ordinary 3-D space, each in its own domain with a
free boundary, relaxed downhill in the ordinary Coulomb energy. One CPU solver, live in your browser
— no wavefunction on configuration space, just charge.
// RealQM — each electron is a charge cloud u(x) in its own non-overlapping domain (Neumann interface):
u ← u + dt·[ ½∇²u + (K − 2P)·u ] relax downhill: kinetic + kernels K − repulsion 2P
P ← P + dt·[ ∇²P + 2π·u_other² ] P = the OTHER cloud's Coulomb potential (Poisson)
u ← u / √∫u² one electron per cloud; the bond = charge that feels BOTH kernels
Each stage runs the same imaginary-time relaxation
(u ← u + dt·[½∇·(w∇u) + (K − 2P)·w·u]), with the free boundary tracked as a moving
front. The energy converges over a few thousand steps — watch the E line settle.
Solver adapted from h2_p5_original.html.