5 shells
4 shells
Conjecture: Densest Packing of 37 Congruent Circles in a Circle
Maybe not quite, but close:
http://hydra.nat.uni-magdeburg.de/packing/cci/cci37.html
Hydrogen in a constant magnetic field
from vpython import * scene.fullscreen = True G = 10 # Coulomb constant in analogy to gravitational constant # edit initial conditions here ########## spheres = [ sphere(pos=vector(0,0,0),radius =6,color=color.red,charge=1000,mass=7200,velocity=vector(0,0,0),a = vector(0,0,0),trail=curve(color=color.red)), sphere(pos=vector(0,100,-1),radius=2,color=color.blue,charge=-1,mass=1,velocity=vector(10,0,0),a=vector(0,0,0),trail=curve(color=color.blue)), #sphere(pos=vector(0,12,0),radius=.08,color=color.green,mass=sqrt(4),velocity=vector(1.2,0,0.6),a=vector(0,0,0),trail=curve(color=color.green)), #sphere(pos=vector(0,100,1),radius=2,color=color.white,charge=-1,mass=1,velocity=vector(-10,0,0),a=vector(0,0,0),trail=curve(color=color.white)), #sphere(pos=vector(0,28,0),radius=.4,color=color.orange,mass=sqrt(80),velocity=vector(0.7,0,0.4),a=vector(0,0,0),trail=curve(color=color.orange)), #sphere(pos=vector(0,32,0),radius=0.2,color=color.white,mass=-sqrt(10),velocity=vector(1.5,0,0.4),a=vector(0,0,0),trail=curve(color=color.white)) ] B=arrow(color=color.green,axis=vec(0,10,0)) def acceleration1on2(sphere2,sphere1): r = sphere2.pos - sphere1.pos r_mag = mag(r) normal_r = norm(r) g = ((G*sphere1.charge*sphere2.charge)/pow(r_mag,2))/sphere2.mass*normal_r return g t = 0 dt = .5 # trade-off between simulation speed and numerical accuracy while 1: rate(100) for i in spheres: i.a = vector(0,0,0) soi = vector(0,0,0) for j in spheres: if i!=j: i.a = i.a + acceleration1on2(i,j) spheres[1].a += .001*cross(spheres[1].velocity, B.axis) # Lorentz force due to constant magnetic field for i in spheres: i.velocity = i.velocity + i.a *dt i.pos = i.pos+i.velocity*dt i.trail.append(pos=i.pos) scene.center=vector(spheres[0].pos.x,spheres[0].pos.y,spheres[0].pos.z)
New ideas for a deterministic relativistic model of spin in accordance with the Stern-Gerlach-experiment
Stroboscopic Interpretation of Quantum Mechanics
We can’t determine the position of a particle at one “moment” because it’s moving too fast.