Spinfunktion

Spinfunktion is a term used in physics, particularly in German-language discussions of quantum mechanics, to denote a function that encodes the spin degree of freedom of a quantum system. In non-relativistic quantum mechanics, the spin state of a particle with spin s is described by a spin function, or spinor, which is a vector in a (2s+1)-dimensional Hilbert space. For a spin-1/2 particle, the spinfunktion is a two-component spinor ψ = [α, β]^T, where α and β are complex amplitudes for the eigenstates of the spin projection along a chosen axis (often S_z). Any state can be written as a linear combination α|↑⟩ + β|↓⟩.

The spinfunktion transforms under rotations according to the SU(2) group, with spin operators represented by the Pauli matrices. The Bloch-sphere representation maps pure spin-1/2 states to points on the unit sphere, with the state vector parameterized by polar and azimuthal angles (θ, φ). For higher spins, the spinfunktion has 2s+1 components and obeys corresponding rotation representations.

In quantum field theory, spinor fields such as the Dirac spinor ψ(x) are spacetime-dependent spinfunktion objects, carrying spinor indices and satisfying field equations like the Dirac equation. Spinfunktion concepts underpin areas including atomic physics, quantum information (qubits), and spintronics.