Good quantum number in the context of Observable

⭐ Core Definition: Good quantum number

In quantum mechanics, the eigenvalue $q$ of an observable $O$ is said to be a good quantum number if the observable $O$ is a constant of motion. In other words, the quantum number is good if the corresponding observable commutes with the Hamiltonian. If the system starts from the eigenstate with an eigenvalue $q$ , it remains on that state as the system evolves in time, and the measurement of $O$ always yields the same eigenvalue $q$ .

Good quantum numbers are often used to label initial and final states in experiments. For example, in particle colliders:

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⭐ Core Definition: Good quantum number
Good quantum number in the context of Quantum number
Good quantum number in the context of Term symbol

Good quantum number in the context of Quantum number

In quantum physics and chemistry, quantum numbers are quantities that characterize the possible states of the system. To fully specify the state of the electron in a hydrogen atom, four quantum numbers are needed. The traditional set of quantum numbers includes the principal, azimuthal, magnetic, and spin quantum numbers. To describe other systems, different quantum numbers are required. For subatomic particles, one needs to introduce new quantum numbers, such as the flavour of quarks, which have no classical correspondence.

Quantum numbers are closely related to eigenvalues of observables. When the corresponding observable commutes with the Hamiltonian of the system, the quantum number is said to be "good", and acts as a constant of motion in the quantum dynamics.

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Good quantum number in the context of Term symbol

In atomic physics, a term symbol is an abbreviated description of the total spin and orbital angular momentum quantum numbers of the electrons in a multi-electron atom. So while the word symbol suggests otherwise, it represents an actual value of a physical quantity.

For a given electron configuration of an atom, its state depends also on its total angular momentum, including spin and orbital components, which are specified by the term symbol. The usual atomic term symbols assume LS coupling (also known as Russell–Saunders coupling) in which the all-electron total quantum numbers for orbital (L), spin (S) and total (J) angular momenta are good quantum numbers.

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Good quantum number in the context of Observable

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⭐ Core Definition: Good quantum number

Good quantum number in the context of Quantum number

Good quantum number in the context of Term symbol