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In particle physics, the doublet–triplet (splitting) problem is a problem of some Grand Unified Theories, such as SU(5), SO(10), and . Grand unified theories predict Higgs bosons (doublets of S U ( 2 ) {\displaystyle SU(2)} ) arise from representations of the unified group that contain other states, in particular, states that are triplets of ...
The ability of positronium to form both singlet and triplet states is described mathematically by saying that the product of two doublet representations (meaning the electron and positron, which are both spin-1/2 doublets) can be decomposed into the sum of an adjoint representation (the triplet or spin 1 state) and a trivial representation (the ...
Examples of atoms in singlet, doublet, and triplet states. In quantum mechanics, a triplet state, or spin triplet, is the quantum state of an object such as an electron, atom, or molecule, having a quantum spin S = 1. It has three allowed values of the spin's projection along a given axis m S = −1, 0, or +1, giving the name "triplet".
In quantum mechanics, a doublet is a composite quantum state of a system with an effective spin of 1/2, such that there are two allowed values of the spin component, −1/2 and +1/2. Quantum systems with two possible states are sometimes called two-level systems .
The triplet consists of three states with spin components +1, 0 and –1 along the direction of the total orbital angular momentum, which is also 1 as indicated by the letter P. The total angular momentum quantum number J can vary from L+S = 2 to L–S = 0 in integer steps, so that J = 2, 1 or 0.
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Left: when 2 J-coupling constants are sufficiently unequal (Jab>Jbc) for spin ½ nuclei, a doublet of doublets with an intensity ratio of about 1:1:1:1 is seen in NMR spectra. Right: when Jab=Jbc for spin ½ nuclei, a triplet (collapsed or overlapping doublet of doublets) with an intensity ratio of about 1:2:1 is always seen in NMR spectra.