Search results
Results from the WOW.Com Content Network
In simpler terms, the total angular momentum operator characterizes how a quantum system is changed when it is rotated. The relationship between angular momentum operators and rotation operators is the same as the relationship between Lie algebras and Lie groups in mathematics, as discussed further below. The different types of rotation ...
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.
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]
Examples are the angular momentum of an electron in an atom, electronic spin, and the angular momentum of a rigid rotor. In all cases, the three operators satisfy the following commutation relations, [,] =, [,] =, [,] =, where i is the purely imaginary number and the Planck constant ħ has been set equal to one. The Casimir operator
Examples of vector operators are the momentum, the position, the orbital angular momentum, , and the spin angular momentum, . (Fine print: Angular momentum is a vector as far as rotations are concerned, but unlike position or momentum it does not change sign under space inversion, and when one wishes to provide this information, it is said to ...
One important aspect of quantum mechanics is the occurrence of—in general—non-commuting operators which represent observables, quantities that can be measured. A standard example of a set of such operators are the three components of the angular momentum operators, which are crucial in many quantum systems. These operators are complicated ...
Likewise, the momentum vector is the velocity vector (a polar vector) times mass (a scalar), so is a polar vector. Angular momentum is the cross product of a displacement (a polar vector) and momentum (a polar vector), and is therefore a pseudovector. Torque is angular momentum (a pseudovector) divided by time (a scalar), so is also a pseudovector.
Due to the conservation of angular momentum and the nature of the angular momentum operator, the total angular momentum is always the sum of the individual angular momenta of the electrons, or [6] = + Spin-Orbit interaction (also known as spin-orbit coupling) is a special case of angular momentum coupling.