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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 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.
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 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 cease and desist.
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.
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".