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# 3.1 Spin-½ particles

Experiments show that electrons have an intrinsic property which is called spin. (Mass and charge are other examples of intrinsic properties of particles.) Spin is a type of angular momentum with a quantum number of ½ which means that a measurement of spin along an axis can only have values of or as an outcome. (Here where h is Planck’s constant, 6.626 × 10-34 J s.) Thus, electrons are referred to as spin-½ particles.

The most important spin operators are the component of spin angular momentum in the z-direction, and the total spin angular momentum, . The eigenvalue equations for these operators are

where the angled bracket, is used and is called a ket. represents the eigenfunction, known as an eigenstate with a spin quantum number of and a spin magnetic quantum number of . For a single electron and . The state with is the spin-up state and the state with is the spin-down state.

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