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Almost all operators encountered in quantum mechanics are linear
operators. A linear operator is an operator which satisfies the following
two conditions:
where is a constant and and are functions.
As an example, consider the operators and .
We can see that is a linear operator because
However, is not a linear operator because

(47) 
The only other category of operators relevant to quantum mechanics is the
set of antilinear operators, for which

(48) 
Timereversal operators are antilinear (cf. Merzbacher
[2], section 1611).
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Up: Operators
Previous: Basic Properties of Operators
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David Sherrill
20060815