If we take your hydrogen simulation
(http://users.accesscomm.ca/john/H.GIF), the path of your electron
looks like the path of the tip of a freely rotating arrow (a vector).
For your helium atom (http://users.accesscomm.ca/john/He.GIF), if you
connect both electrons, you have a freely rotating dumb-bell. This type
of motion (Poinsot motion) is well known in the calculations of
attitude of earth satellites.
Freely rotating arrows have two rotational degrees of freedom. The
rotational motion of an arrow is the combination of two rotations:
- a spinning rotation omega-s about the symmetry axis, also called the
figure axis,
- a precession rotation omega-z of the figure axis about a fixed
precession axis, which is your z-axis.
The time dependence |psi(t)> of the vector representing the arrow is
given by equation (9) in
http://materion.free.fr/physique/QMObservationMacroscopicArrows.pdf.
An interesting suggestive feature is that the projection of omega-s on
the z-axis is a constant. For an angle theta=pi/3 between the figure
axis and the z-axis, this constant is 1/2 or -1/2. In other words, the
projection of spin omega-s of |psi(t)> is quantized and may take only
two values +1/2 or -1/2. This result is obtained with ordinary everyday
objects, like arrows, needles or rods. There is nothing weird about
such quantum behaviour.
In response to Daniel Pitts above:
> Electrons don't "orbit" the nucleas, they "exist around" the nucleas
the tip of an arrow may orbit the nucleus while the hard matter of the
arrow just exists around the nucleus.
By the way, I noticed the similarity between your model (based on a
curtate cycloid) and the hubius helix in
http://www.arxiv.org/abs/physics/0512265 and reported by fredifizzx
(http://groups.google.com/group/sci.physics/browse_frm/thread/cb938d22dbc3d4f6/e8
08e1ad14004e58?&hl=en#e808e1ad14004e58).
The Hubius helix is also generated by the tip of a freely rotating
arrow.
--
Arjen Dijksman
--------------------------------
Materion physics, the search for a satisfactory explanation of natural
phenomena at http://materion.free.fr