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An operator is a function over a space of physical states onto another space of states. The simplest example of the utility of operators is the study of symmetry (which makes the concept of a group useful in this context).
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]
In quantum mechanics, energy is defined in terms of the energy operator, acting on the wave function of the system as a consequence of time translation symmetry. Definition [ edit ]
In physics, an observable is a physical property or physical quantity that can be measured.In classical mechanics, an observable is a real-valued "function" on the set of all possible system states, e.g., position and momentum.
[2] A nice way to double-check that these relations are correct is to do a Taylor expansion of the translation operator acting on a position-space wavefunction. Expanding the exponential to all orders, the translation operator generates exactly the full Taylor expansion of a test function: = ^ () = (^) = (=!
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 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.
Curl, (with operator symbol ) is a vector operator that measures a vector field's curling (winding around, rotating around) trend about a given point. As an extension of vector calculus operators to physics, engineering and tensor spaces, grad, div and curl operators also are often associated with tensor calculus as well as vector calculus.