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Encyclopedia > Operator (physics)

In mathematical formulations of quantum mechanics, an operator is a linear transformation from a Hilbert space to itself. An observable is a self-adjoint operator. By extension, operator is also used to refer to an element of a C* algebra. For the justitication of this usage, see Gelfand-Naimark theorem


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Operator - Wikipedia, the free encyclopedia (0 words)
Operators are often in practice just partial functions, a common phenomenon in the theory of differential equations since there is no guarantee that the derivative of a function exists.
It is another integral operator; it is useful mainly because it converts a function on one (spatial) domain to a function on another (frequency) domain, in a way that is effectively invertible.
Three main operators are key to vector calculus, the operator ∇, known as gradient, where at a certain point in a scalar field forms a vector which points in the direction of greatest change of that scalar field.
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