Operators

The word operator sees use in at least two different ways.

We say that both addition and multiplication are binary operations and therefore the symbols + and * can be called operators.

This is not the interpretation that interests us for this article. Instead, here, we say that a function takes a number and returns another function. We then say that an operator takes a function and returns another function.

F(2)=4

D(x^2)=2x

Hopefully you guessed that the function was f(x)=2x and you guessed that the operator was \dfrac {d}{dx} .

Operators are applied working from right to left.

(\hat{A} + \hat{B}) f(x) = \hat{A} f(x)+ \hat{B} f(x)

The multiplication of Operators is Associative.

(\hat{A} \hat{B}) \hat{C} f(x) = \hat{A} (\hat{B} \hat{C}) f(x)