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  2. Angular momentum operator - Wikipedia

    en.wikipedia.org/wiki/Angular_momentum_operator

    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 ...

  3. Pauli–Lubanski pseudovector - Wikipedia

    en.wikipedia.org/wiki/Pauli–Lubanski_pseudovector

    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 LubaƄski. [1] It describes the spin states of moving particles. [2]

  4. Momentum operator - Wikipedia

    en.wikipedia.org/wiki/Momentum_operator

    The momentum operator can be described as a symmetric (i.e. Hermitian), unbounded operator acting on a dense subspace of the quantum state space. If the operator acts on a (normalizable) quantum state then the operator is self-adjoint. In physics the term Hermitian often refers to both symmetric and self-adjoint operators. [7] [8]

  5. Angular momentum - Wikipedia

    en.wikipedia.org/wiki/Angular_momentum

    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.

  6. Ladder operator - Wikipedia

    en.wikipedia.org/wiki/Ladder_operator

    A particular application of the ladder operator concept is found in the quantum-mechanical treatment of angular momentum. For a general angular momentum vector J with components J x, J y and J z one defines the two ladder operators [3] + = +, =, where i is the imaginary unit.

  7. Casimir element - Wikipedia

    en.wikipedia.org/wiki/Casimir_element

    In mathematics, a Casimir element (also known as a Casimir invariant or Casimir operator) is a distinguished element of the center of the universal enveloping algebra of a Lie algebra. A prototypical example is the squared angular momentum operator , which is a Casimir element of the three-dimensional rotation group .

  8. Holstein–Primakoff transformation - Wikipedia

    en.wikipedia.org/wiki/Holstein–Primakoff...

    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 ...

  9. Operator (physics) - Wikipedia

    en.wikipedia.org/wiki/Operator_(physics)

    The wavefunction must be square-integrable ... (such as position, momentum, energy, angular momentum etc.). If ... Since this is a vector and operator equation, if ...