By analogy with the results for orbital angular momentum (or more generally for quantum angular momentum), there exists for the spin operator a basis of eigenvectors called | indicates s , m s ⟩ {displaystyle |s,m_{s}rangle } , where s {displaystyle s} is an integer or half integer and m s {displaystyle m_{s}} is an integer or half integer which is one of the values 2 s + 1 {displaystyle 2s+1} − s ≤ m s ≤ s {displaystyle -, sleq m_{s}leq s}, such as: Here are words that are often used in combination with spin. Thus, the spin is a Hermitian vector operator S^{displaystyle {hat {S}}} with three components, commonly denoted S^x, S^y {displaystyle {hat {S}}_{x},,{hat {S}}_{y}} and S^ z {displaystyle {hat {S}}_{z}} with reference to the three axes of Cartesian coordinates usable in physical space. These components are observable that verify the commutation relations characteristic of angular momentum[9]: According to this representation, each 1/2 spin state finds a general©© representation©© (see figure opposite). © The vector that passes through the origin and points to the projection (The map projection is a set of techniques for representing©the surface of…) of the complex u on the Riemann spher, gives a general©©visualization of the state of spin 1/2 as direction©in space©. As the spin statistics theorem shows, the integer or half-integer value of spin determines a crucial property of the particle: The spin of composite© particles, such as the proton, neutron, atomic nucleus (The atomic nucleus refers to the region at the center of an atom, consisting of…) or the atom (An atom (Ancient Greek ἄομος [atomos], “that… “), © consists of the spins of the particles, from which they are composed, plus the angular momentum of the particles©©relative to each other. Spin has important theoretical and practical implications, it affects virtually the entire physical world. It is responsible for the magnetic spin moment and therefore the resulting anomalous Zeeman effect (sometimes mistakenly called abnormal). Home > Dictionary > Definitions of the word “spin” The vector S → {displaystyle {vec {S}}}, defined by the three projections ( ⟨ S x ⟩ , ⟨ S y ⟩ , ⟨ S z ⟩ ) {displaystyle {big (}langle S_{x}rangle ,langle S_{y}rangle ,langle S_{z}rangle {big )}} describes a “direction” at which the median direction of the angular momentum of the spin points, and which is wisely called polarization. [17] It is exactly the orientation of this vector that was previously represented on the Riemann or Bloch sphere. It turns out that this spin polarization vector has practical physical significance, especially in nuclear magnetic resonance (NMR) spectroscopy. In this technique, the spins of protons (or any other atomic nucleus with non-zero spin) can be produced in any state. If, for example, the spin system is placed in a homogeneous magnetic field, the average polarization in thermodynamic equilibrium corresponds to the state | ↑ ⟩ {displaystyle |uparrow rangle }. The application of selected high-frequency pulses then makes it possible to polarize the spins in any other spatial direction.
[17] The maximum NMR signal is obtained when the sensing coil is aligned according to the direction of this polarization. In the case of the electron, electron paramagnetic resonance spectroscopy (EPR) is based on exactly the same principles. In 1927, Wolfgang Pauli proposed spin modeling in matrix terms, which corresponds to a writing in the form of operators on the wave function of the Schrödinger equation: the Pauli equation. In 1928, Paul Dirac used the Klein–Gordon equation to show that a non-zero spin particle confirms a relativistic equation now called the Dirac equation. It is not always easy to derive the spin of a particle from simple principles; For example, although the proton is known to have a spin of 1/2, the question of how the elementary particles that compose it are arranged and arranged is still an active subject of research (see spin structure of nucleons). [11] [12].
