Particles have intrinsic properties such as mass and charge. Spin is another fundamental property of particles, distinct from mass and charge.

The concept of spin was first discovered through the Stern-Gerlach experiment:

Setup.
Electrically neutral silver atoms (with 1 valence electron) were shot through a non-uniform magnetic field.

Expectation
Since silver atoms had zero orbital angular momentum, they were not expected to interact with the magnetic field and were predicted to pass through undeflected.

Observation
The beam split into two distinct paths, indicating that electrons possess intrinsic angular momentum (spin), which is quantized.

Properties of spin

1. Quantization: Spin is quantized, meaning it can only take specific discrete values. For electrons, the spin value is ½.

2. Directionality: The magnitude of spin is fixed for a given particle. The direction of spin can point in any orientation, but it can only be measured along one axis at a time. Measuring spin along one axis destroys information about its orientation along other axes.

3. Wavefunction Rotation: The spin value determines the angle of rotation required for the particle’s wavefunction to return to its original state.

For spin-½ particles (e.g., electrons, protons, neutrons, neutrinos, quarks), the wavefunction returns to itself only after two full rotations (720°).

Spin and Magnetic Behavior

Particles with spin behave like tiny magnets. In a magnetic field, particles with spin experience a force, causing them to follow specific trajectories. The Stern-Gerlach experiment demonstrated this by splitting the beam into two distinct paths, corresponding to the two possible spin states (spin-up and spin-down).

Angular Momentum and Spin
Spin is a form of intrinsic angular momentum, independent of orbital motion. Faster “spinning” corresponds to greater angular momentum, represented by a larger vector.

Spin and the Pauli Exclusion Principle
Particles with half-integer spin (e.g., electrons) obey the Pauli Exclusion Principle, which states that no two identical fermions can occupy the same quantum state simultaneously. This principle is fundamental to the structure of atoms and the behavior of matter.