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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 ...
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 .
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
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 ...
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
This splitting is called fine structure. The splitting is larger for atoms with higher atomic number. The splitting decreases towards the series limit. Another splitting occurs on the redder line of the doublet. This is because of splitting in the D level and . Splitting in the D level has a lesser amount than the P level, and it reduces as the ...
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The most common tuplet [9] is the triplet (German Triole, French triolet, Italian terzina or tripletta, Spanish tresillo).Whereas normally two quarter notes (crotchets) are the same duration as a half note (minim), three triplet quarter notes have that same duration, so the duration of a triplet quarter note is 2 ⁄ 3 the duration of a standard quarter note.