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fsh26

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- TL;DR Summary
- A discussion of the derivation of Majorana representation formulas for spins greater than 1/2 is proposed.

In the article by E. Majorana "Oriented atoms in a variable magnetic field", in particular, it's considered (and solved) the problem of describing a state with spin

That is, if
the general state of the spin system

, (1)

then, according to the article, those 2J points in on the Bloch sphere are described by the following complex numbers (
):

. (2)

Here
- is the angle between the unit vector and the Z axis,
- is the angle between the projection of the given vector (on the XY plane) with the X axis (Bloch spheres),
- are the roots of the polynomial

, (3)

where

. (4)

In the case of J=1/2, is very simple

(5)

Here
(
) can be considered as the probability of finding the end of the unit vector at the lower (upper) pole of the Bloch sphere, and
- is a point of the complex plane that is drawn through the center given sphere (stereographic projection of the end of the unit vector from the south pole onto the given plane).

**J**using**2J**points on the Bloch sphere.That is, if

then, according to the article, those 2J points in on the Bloch sphere are described by the following complex numbers (

Here

where

In the case of J=1/2, is very simple

Here

__But, for the cases J>1/2, I encountered difficulties in following the idea of deriving (3) and (4).__Of course, there are several papers where this representation of Majorana is used, but so far I have not found such a work where the derivation of formulas is discussed in detail. I will be grateful if you advise literature or sources that can help to clearly understand the derivation of formulas (3) and (4).