Operators

Levine [3] defines an operator as ``a rule that transforms a given function into another function'' (p. 33). The differentation operator $d/dx$ is an example--it transforms a differentiable function $f(x)$ into another function $f'(x)$. Other examples include integration, the square root, and so forth. Numbers can also be considered as operators (they multiply a function). McQuarrie [1] gives an even more general definition for an operator: ``An operator is a symbol that tells you to do something with whatever follows the symbol'' (p. 79). Perhaps this definition is more appropriate if we want to refer to the ${\hat C}_3$ operator acting on NH$_3$, for example.