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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.
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.)
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]
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 ...
An operator is a function over a space of physical states onto another space of states. ... The momentum operator in position basis in one dimension is: ^ = ...
The operator R internal, related to S, rotates the particles' internal spin states without changing their positions. Just as J is the generator for rotation operators , L and S are generators for modified partial rotation operators.
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The translation operator ^ moves particles and fields by the amount .Therefore, if a particle is in an eigenstate | of the position operator (i.e., precisely located at the position ), then after ^ = | + | acts on it, the particle is at the position +: ^ | = | + .
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