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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 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.
In physics and chemistry, the spin quantum number is a quantum number (designated s) that describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particle. It has the same value for all particles of the same type, such as s = 1 / 2 for all electrons.
The trivial case of the angular momentum of a body in an orbit is given by = where is the mass of the orbiting object, is the orbit's frequency and is the orbit's radius.. The angular momentum of a uniform rigid sphere rotating around its axis, instead, is given by = where is the sphere's mass, is the frequency of rotation and is the sphere's radius.
The total angular momentum of light consists of two components, both of which act in a different way on a massive colloidal particle inserted into the beam. The spin component causes the particle to spin around its axis, while the other component, known as orbital angular momentum (OAM), causes the particle to rotate around the axis of the beam.
The classical definition of angular momentum is =.The quantum-mechanical counterparts of these objects share the same relationship: = where r is the quantum position operator, p is the quantum momentum operator, × is cross product, and L is the orbital angular momentum operator.
A spin- 1 / 2 particle is characterized by an angular momentum quantum number for spin s of 1 / 2 . In solutions of the Schrödinger equation, angular momentum is quantized according to this number, so that total spin angular momentum
"Vector cones" of total angular momentum J (purple), orbital L (blue), and spin S (green). The cones arise due to quantum uncertainty between measuring angular momentum component. Due to the spin–orbit interaction in an atom, the orbital angular momentum no longer commutes with the Hamiltonian, nor does the spin. These therefore change over time.