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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 ()) arise from representations of the unified group that contain other states, in particular, states that are triplets of color.
Examples of atoms in singlet, doublet, and triplet states.. 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.
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.
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 ...
Another example of nearly synonymous doublets is aperture and overture (the commonality behind the meanings is "opening"). Doublets may also develop contrasting meanings, such as the terms host and guest, which come from the same PIE word * gʰóstis and already existed as a doublet in Latin, and then Old French, [2] before being borrowed into ...
The spectrum would have two signals, each being a doublet. Each doublet will have the same area because both doublets are produced by one proton each. The two doublets at 1 ppm and 2.5 ppm from the fictional molecule CH−CH are now changed into CH 2 −CH: The total area of the 1 ppm CH 2 peak will be twice that of the 2.5 ppm CH peak.
A legal doublet is a standardized phrase used frequently in English legal language consisting of two or more words that are irreversible binomials and frequently synonyms, usually connected by "and", such as "null and void".
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".