quantumspins

Quantum spins describe intrinsic angular momentum of elementary particles and composite systems, distinct from orbital angular momentum, and are characterized by the spin quantum number s with projections m_s ranging from -s to +s.

In spin-1/2 systems, states form a two-level basis; spin operators are S_i = (ħ/2) σ_i, where σ_i are the Pauli matrices. For general spin s, the state space has dimension 2s+1 and the spin operators satisfy the SU(2) algebra.

Measurements yield discrete outcomes corresponding to eigenvalues of the spin projection along a chosen axis. The Stern-Gerlach experiment demonstrated spin quantization. Magnetic moments couple to external fields via H = -γ B · S; Zeeman splitting divides energy levels according to m_s.

Entanglement and quantum information: spins serve as qubits; two or more spin systems can be entangled. Spin chains model magnetic interactions through the Heisenberg exchange; implementation platforms include nitrogen-vacancy centers in diamond and semiconductor quantum dots; coherence times govern performance.

In condensed matter, collective spin excitations called magnons emerge from ordered spin systems; exchange interactions produce ferromagnetism or antiferromagnetism. Spintronics relies on electron spin for information processing and memory.

In particle physics, particles with half-integer spin are fermions, while integer spin denotes bosons; the spin-statistics theorem relates spin to quantum statistics. Angular momenta combine via Clebsch–Gordan coefficients to form total spin states used in spectroscopy and reactions.