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In quantum mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role in the theory of atomic and molecular physics and other quantum problems involving rotational symmetry. Being an observable, its eigenfunctions represent the ...
Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity – the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved.
Wigner–Eckart theorem. The Wigner–Eckart theorem is a theorem of representation theory and quantum mechanics. It states that matrix elements of spherical tensor operators in the basis of angular momentum eigenstates can be expressed as the product of two factors, one of which is independent of angular momentum orientation, and the other a ...
The total angular momentum operators can be shown to satisfy the very same commutation relations, [,] = , where k, l, m ∈ {x, y, z}. Indeed, the preceding construction is the standard method [ 4 ] for constructing an action of a Lie algebra on a tensor product representation.
Holstein–Primakoff transformation. In quantum mechanics, the Holstein–Primakoff transformation is a mapping from boson creation and annihilation operators to the spin operators, effectively truncating their infinite-dimensional Fock space to finite-dimensional subspaces. One important aspect of quantum mechanics is the occurrence of—in ...
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 ...
The total angular momentum operator is the sum of the orbital and spin ... "Position and momentum in quantum mechanics" (PDF). Lie groups; Porter, F. (2009).
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