Quantum number

A quantum number is any one of a set of numbers used to specify the full quantum state of any system in quantum mechanics. Each quantum number specifies the value of a conserved quantity in the dynamics of the quantum system. Since any quantum system can have one or more quantum numbers, it is a futile job to list all possible quantum numbers. This article therefore illustrates the concepts by choosing two well-known examples, after a brief introduction to the general concept of quantum numbers.

Elementary particles

For a more complete description of the quantum states of elementary particles see the articles on the standard model and flavour (particle physics).

Related Topics:
Standard model - Flavour (particle physics)

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Elementary particles contain many quantum numbers which are usually said to be intrinsic to them. However, it should be understood that the elementary particles are quantum states of the standard model of particle physics, and hence the quantum numbers of these particles bear the same relation to the Hamiltonian of this model as the quantum numbers of the Bohr atom does to its Hamiltonian. In other words, each quantum number denotes a symmetry of the problem. It is more useful in field theory to distinguish between spacetime and internal symmetries.

Related Topics:
Quantum state - Standard model - Particle physics - Bohr atom - Field theory - Spacetime - Internal

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Typical quantum numbers related to spacetime symmetries are spin (related to rotational symmetry), the parity, C-parity and T-parity (related to the Poincare symmetry of spacetime). Typical internal symmetries are lepton number and baryon number or the electric charge. For a full list of quantum numbers of this kind see the article on flavour.

Related Topics:
Spin - Parity - C-parity - T-parity - Poincare symmetry - Spacetime - Lepton number - Baryon number - Electric charge - Flavour

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It is worth mentioning here a minor but often confusing point. Most conserved quantum numbers are additive. Thus, in an elementary particle reaction, the sum of the quantum numbers should be the same before and after the reaction. However, some, usually called a parity, are multiplicative; ie, their product is conserved. All multiplicative quantum numbers belong to a symmetry (like parity) in which applying the symmetry transformation twice is equivalent to doing nothing. These are all examples of an abstract group called Z2.

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