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Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms. [1] [2]: 183–184 Spin is quantized, and accurate models for the interaction with spin require relativistic quantum mechanics or quantum field theory.
The phrase spin quantum number refers to quantized spin angular momentum. The symbol s is used for the spin quantum number, and m s is described as the spin magnetic quantum number [3] or as the z-component of spin s z. [4] Both the total spin and the z-component of spin are quantized, leading to two quantum numbers spin and spin magnet quantum ...
This is the basis for saying conservation of angular momentum is a general principle of physics. For a particle without spin, J = L, so orbital angular momentum is conserved in the same circumstances. When the spin is nonzero, the spin–orbit interaction allows angular momentum to transfer from L to S or back.
Given a unit vector in 3 dimensions, for example (a, b, c), one takes a dot product with the Pauli spin matrices to obtain a spin matrix for spin in the direction of the unit vector. The eigenvectors of that spin matrix are the spinors for spin-1/2 oriented in the direction given by the vector. Example: u = (0.8, -0.6, 0) is a unit vector ...
In the simple case where we consider the vector space , a ket can be identified with a column vector, and a bra as a row vector. If, moreover, we use the standard Hermitian inner product on C n {\displaystyle \mathbb {C} ^{n}} , the bra corresponding to a ket, in particular a bra m | and a ket | m with the same label are conjugate transpose .
In physics, angular velocity (symbol ω or , the lowercase Greek letter omega), also known as the angular frequency vector, [1] is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction.
In physics, the Pauli–Lubanski pseudovector is an operator defined from the momentum and angular momentum, used in the quantum-relativistic description of angular momentum. It is named after Wolfgang Pauli and Józef Lubański. [1] It describes the spin states of moving particles. [2]
The general expression for the spin angular momentum is [1] =, where is the speed of light in free space and is the conjugate canonical momentum of the vector potential.The general expression for the orbital angular momentum of light is =, where = {,,,} denotes four indices of the spacetime and Einstein's summation convention has been applied.