In quantum mechanics, spin is an analog of the familiar phenomenon of the same name. Elementary particles have an intrinsic amount of spin that is either a whole number or half a whole number (in multiples of Planck's constant), and which never changes. Spin is one of the quantum numbers by which a particle is specified.
The existence of spin first became apparent during attempts to explain the multiplet structure (or fine structure) of spectra. For example, it had been recognized for many years that the yellow sodium line and the remaining members of the whole of its series are close doubles (see D lines). Since the already-known quantum numbers n (principal quantum number) and l (azimuthal quantum number), couldn't by themselves account for multiplet structure, Samuel Goudsmit and George Ühlenbeck in 1926 put forward the theory of electron spin. According to this every electron has a spin of (1/2)(h/2π). This spin gives rise to a magnetic moment and as the orbital rotation of the electron also produces a magnetic moment these two will interact. The spin angular moment, denoted by the quantum number s, and having the value (1/2) in the case of the electron, can combine vectorially with the orbital angular momentum l to form a resultant denoted by the quantum number j, which represents the total angular momentum of the electron. The vector addition is usually shown as j = l ± s, the addition being quantized.
Isotopic spin is a mathematical quantity related to the number of different charges in a particle family. Isotopic spin, or isospin, describes the electric charge of a particle by the orientation of a hypothetical spin vector in an abstract charge space. The charge independence of nuclear forces is then described by the invariance of the equations describing them under rotations of the isospin vector in this abstract charge space.