#### How to represent a spin 1/2

The above simulation shows the state of a spin-1/2 particle. The state is described
through a unit vector, shown in yellow, pointing in the direction of the average
value of the spin vector.
You can change the frame orientation by dragging the bounding sphere with the mouse.
You can also change the spin state, either by entering new q
and j values with the keyboard, or by dragging the yellow
arrow with the mouse, the Ctrl key being pushed down.

Note that
j and j +2p
yield the same unit vector while they correspond to opposite states in the Hilbert
space. In other words, you need to turn 4p for recovering
the same state.
As in the case of a propagating wavepacket, it
should be mentioned that in quantum mechanics it is impossible to
directly observe the entire state of the system as the above
simulation might lead to believe. Indeed, it is impossible to
simulatenously measure the different cartesian components of the
spin vector.
Therefore, you should take this as the simulation of a mathematical
object
- the system state - which cannot be directly observed for a single
spin. However, if you have a large assembly of spins all prepared
in the same state, you can measure each cartesian component for a
third of the ensemble and hence measure the average spin vector.
This general remark also holds for the spin simulations shown
hereafter.

**
Note that this version is obsolete. Please see the new version.
**