Spin triplet

In quantum mechanics, a triplet is a quantum state of a system with a spin of 1, such that there are three allowed values of the spin component: −1, 0 and +1.

Spin, in the context of quantum mechanics, is not a mechanical rotation but a more abstract concept that characterizes a particle's intrinsic angular momentum. It is particularly important for systems at atomic length scales, such as individual atoms, protons, or electrons.

Almost all molecules encountered in daily life exist in a singlet state, but molecular oxygen is an exception. At room temperature, O₂ exists in a triplet state, which can only undergo a chemical reaction by making the forbidden transition into a singlet state. This makes it kinetically nonreactive despite being thermodynamically a strong oxidant. Photochemical or thermal activation can bring it into the singlet state, which makes it kinetically as well as thermodynamically a strong oxidant.

In a system with two spin-1/2 particles - for example the proton and electron in the ground state of hydrogen, measured on a given axis, each particle can be either spin up or spin down so the system has four basis states in all

using the single particle spins to label the basis states, where the first arrow and second arrow in each combination indicate the spin direction of the first particle and second particle respectively.

More rigorously

where ${\displaystyle s_{1}}$ and ${\displaystyle s_{2}}$ are the spins of the two particles, and ${\displaystyle m_{1}}$ and ${\displaystyle m_{2}}$ are their projections onto the z-axis. Since for spin-1/2 particles, the ${\displaystyle |1/2,m\rangle }$ basis states span a 2-dimensional space, the ${\displaystyle |1/2,m_{1}\rangle |1/2,m_{2}\rangle }$ basis states span a 4-dimensional space.

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