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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 ...
For example, the ground state of a carbon atom is 3 P (Term symbol). The superscript three (read as triplet) indicates that the multiplicity 2S+1 = 3, so that the total spin S = 1. This spin is due to two unpaired electrons, as a result of Hund's rule which favors the single filling of degenerate orbitals. The triplet consists of three states ...
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".
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.
In other words, its OK to say that the deltas for a isospin quadruplet, and that the next line down in the decuplet is an isospin triplet of sigmas, and the next one is an isospin doublet of xi's, and finally an isospin singlet omega. But I find the attempted summary of the history to be misleading, by this I mean the section "Observation of ...
The best known example is a spin multiplet, which describes symmetries of a group representation of an SU(2) subgroup of the Lorentz algebra, which is used to define spin quantization. A spin singlet is a trivial representation, a spin doublet is a fundamental representation and a spin triplet is in the vector representation or adjoint ...
Unrestricted Hartree–Fock (UHF) theory is the most common molecular orbital method for open shell molecules where the number of electrons of each spin are not equal. While restricted Hartree–Fock theory uses a single molecular orbital twice, one multiplied by the α spin function and the other multiplied by the β spin function in the Slater determinant, unrestricted Hartree–Fock theory ...
The resulting electron configuration can be described in terms of bond type, parity and occupancy for example dihydrogen 1σ g 2. Alternatively it can be written as a molecular term symbol e.g. 1 Σ g + for dihydrogen. Sometimes, the letter n is used to designate a non-bonding orbital. For a stable bond, the bond order defined as