To determine the value of the quantum state |ψ〉, set the values of the polar and azimuth angles
either using the GUI in the upper right corner of the program, or using the keys located
under the GUI.
Blue arrow - the direction of spin in physical space
Green arrow - the direction of spin in spinor space
In the above visualization, you can set the direction of the electron spin in three-dimensional physical space using two angles.
The first angle, which is given the name of the polar angle θ, sets the (geographical) latitude.
The second sets the azimuth angle φ. Since the value of the polar angle in the spinor space is half
of the corresponding angle in the physical space, the corresponding spinor angle θ/2 is simultaneously set.
Azimuthal angles in both spaces have the same values.
The blue arrow determines the direction
of the electron's spin in physical space. The green arrow determines the direction of the spinor.
The values of the polar and azimuth angles are set in the right part of the window either using the GUI or using the buttons.
In response to this action, the value of the state function and two probabilities corresponding to the spin values +1 and -1 are given.
In the program, you can see the value of the state vector |ψ〉
for any predetermined angle of the electron in the spinor and physical space.
In physical space, the angle θ has a range of variation from 0° to 720°, and in spinor from 0° to 360°.
Therefore, on the sphere, two revolution of θ physical space correspond to one revolution of θ spinor space.
The azimuthal angle φ in both spaces has the same range of variation from 0° to 360°.
Thus, each point on the surface of the sphere defines a unit vector in the spinor space.
The starting points of these vectors are located in the center of the sphere.
The directions along the Z axis are denoted as Up (u) and Down (d).
The directions along the X axis are denoted as Right (r) and Left (l).
The directions along the Y axis are denoted as Forward (f) and Back (b).