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Quantum number

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	Topics Quantum number Topic Home Quantum numbers describe values of conserved numbers in the dynamics of the quantum system. They often describe specifically the energies of electronElectron The electron is a fundamental subatomic particle that carries an electric charge.... s in atomAtom In chemistry and physics, an atom is the smallest possible particle of a chemical element that retains its chemical propert... s, but other possibilities include angular momentumFacts About Angular momentum In physics the angular momentum of an object with respect to a reference point is a measure for the extent to which, and the... , spinSpin (physics) In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the mo... etc. Since any quantum system can have one or more quantum numbers, it is a futile job to list all possible quantum numbers. How Many Quantum Numbers? The question of how many quantum numbers are needed to describe any given system has no universal answer, although for each system one must find the answer for a full analysis of the system. The dynamics of any quantum system are described by a quantum HamiltonianHamiltonian (quantum mechanics) The quantum Hamiltonian is the physical state of a system, which may be characterized as a ray in an abstract Hilbert space ... , H. There is one quantum number of the system corresponding to the energy, i.e., the eigenvalue of the Hamiltonian. There is also one quantum number for each operator O that commutes with the Hamiltonian (i.e. satisfies the relation OH = HO). These are all the quantum numbers that the system can have. Note that the operators O defining the quantum numbers should be independent of each other. Often there is more than one way to choose a set of independent operators. Consequently, in different situations different sets of quantum numbers may be used for the description of the same system. Quantum numbers with spin-orbit interaction When one takes the spin-orbit interactionFacts About Spin-orbit interaction In physics, in the area of quantum mechanics, the spin-orbit interaction is a shift in energy levels due to the potential en... into consideration, l, m and s no longer commuteCommutativity A map or binary operation is said to be commutative when, for any y'' and any z'' in A''... with the HamiltonianHamiltonian (quantum mechanics) The quantum Hamiltonian is the physical state of a system, which may be characterized as a ray in an abstract Hilbert space ... , and their value therefore changes over time. Thus another set of quantum numbers should be used. This set includes The (j = 1/2,3/2 ... n−1/2) gives the total angular momentumFacts About Angular momentum In physics the angular momentum of an object with respect to a reference point is a measure for the extent to which, and the... through the relation . The (m_j = -j,-j+1... j), which is analogous to m, and satisfies . ParityParity (physics) In physics, a parity transformation is the simultaneous flip in the sign of all spatial coordinates:... . This is the eigenvalue under reflection, and is positive (i.e. +1) for states which came from even l and negative (i.e. -1) for states which came from odd l. The former is also known as even parity and the latter as odd parity For example, consider the following eight states, defined by their quantum numbers: (1) l = 1, m_l = 1, m_s = +1/2 (2) l = 1, m_l = 1, m_s = -1/2 (3) l = 1, m_l = 0, m_s = +1/2 (4) l = 1, m_l = 0, m_s = -1/2 (5) l = 1, m_l = -1, m_s = +1/2 (6) l = 1, m_l = -1, m_s = -1/2 (7) l = 0, m_l = 0, m_s = +1/2 (8) l = 0, m_l = 0, m_s = -1/2 The quantum stateQuantum state In quantum mechanics, the quantum state of a system completely describes all aspects of the system.... s in the system can be described as linear combination of these eight states. However, in the presence of spin-orbit interactionSpin-orbit interaction In physics, in the area of quantum mechanics, the spin-orbit interaction is a shift in energy levels due to the potential en... , if one wants to describe the same system by eight states which are eigenvectors of the HamiltonianHamiltonian (quantum mechanics) Summary The quantum Hamiltonian is the physical state of a system, which may be characterized as a ray in an abstract Hilbert space ... (i.e. each represents a state which does not mix with others over time), we should consider the following eight states: j = 3/2, m_j = 3/2, odd parity (coming from state (1) above) j = 3/2, m_j = 1/2, odd parity (coming from states (2) and (3) above) j = 3/2, m_j = -1/2, odd parity (coming from states (4) and (5) above) j = 3/2, m_j = -3/2, odd parity (coming from state (6)) j = 1/2, m_j = 1/2, odd parity (coming from state (2) and (3) above) j = 1/2, m_j = -1/2, odd parity (coming from states (4) and (5) above) j = 1/2, m_j = 1/2, even parity (coming from state (7) above) j = 1/2, m_j = -1/2, even parity (coming from state (8) above) General principles Particle physics See also QuantumQuantum In physics, a quantum refers to an indivisible and perhaps elementary entity.... Quantum mechanicsQuantum mechanics Quantum mechanics is a first quantized quantum theory that supersedes classical mechanics at the atomic and subatomic levels... Quantum field theoryQuantum field theory Quantum field theory is the quantum theory of fields.... Many-worlds interpretationMany-worlds interpretation The many-worlds interpretation of quantum mechanics or MWI, also known as the relative state formulation, the... Interpretation of quantum mechanicsInterpretation of quantum mechanics An interpretation of quantum mechanics is an attempt to answer the question, What exactly is quantum mechanics talking abo...