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  2. Momentum operator - Wikipedia

    en.wikipedia.org/wiki/Momentum_operator

    This operator occurs in relativistic quantum field theory, such as the Dirac equation and other relativistic wave equations, since energy and momentum combine into the 4-momentum vector above, momentum and energy operators correspond to space and time derivatives, and they need to be first order partial derivatives for Lorentz covariance.

  3. Position and momentum spaces - Wikipedia

    en.wikipedia.org/wiki/Position_and_momentum_spaces

    Position space (also real space or coordinate space) is the set of all position vectors r in Euclidean space, and has dimensions of length; a position vector defines a point in space. (If the position vector of a point particle varies with time, it will trace out a path, the trajectory of a particle.)

  4. Position operator - Wikipedia

    en.wikipedia.org/wiki/Position_operator

    In quantum mechanics, the position operator is the operator that corresponds to the position observable of a particle. When the position operator is considered with a wide enough domain (e.g. the space of tempered distributions ), its eigenvalues are the possible position vectors of the particle.

  5. Operator (physics) - Wikipedia

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

    Due to linearity, vectors can be defined in any number of dimensions, as each component of the vector acts on the function separately. One mathematical example is the del operator, which is itself a vector (useful in momentum-related quantum operators, in the table below). An operator in n-dimensional space can be written:

  6. Canonical commutation relation - Wikipedia

    en.wikipedia.org/wiki/Canonical_commutation_relation

    between the position operator x and momentum operator p x in the x direction of a point particle in one dimension, where [x, p x] = x p x − p x x is the commutator of x and p x , i is the imaginary unit, and ℏ is the reduced Planck constant h/2π, and is the unit operator. In general, position and momentum are vectors of operators and their ...

  7. Ehrenfest theorem - Wikipedia

    en.wikipedia.org/wiki/Ehrenfest_theorem

    The Ehrenfest theorem, named after Austrian theoretical physicist Paul Ehrenfest, relates the time derivative of the expectation values of the position and momentum operators x and p to the expectation value of the force = ′ on a massive particle moving in a scalar potential (), [1]

  8. List of equations in classical mechanics - Wikipedia

    en.wikipedia.org/wiki/List_of_equations_in...

    Left: intrinsic "spin" angular momentum S is really orbital angular momentum of the object at every point, right: extrinsic orbital angular momentum L about an axis, top: the moment of inertia tensor I and angular velocity ω (L is not always parallel to ω) [6] bottom: momentum p and its radial position r from the axis.

  9. Symplectic integrator - Wikipedia

    en.wikipedia.org/wiki/Symplectic_integrator

    The set of position and momentum coordinates (,) are called canonical coordinates. (See Hamiltonian mechanics for more background.) The time evolution of Hamilton's equations is a symplectomorphism, meaning that it conserves the symplectic 2-form. A numerical scheme is a symplectic integrator if it also conserves this 2-form.