68111133-3-3-operatorsandcommutators - Operators...

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Operators Commutators in Quantum Physics In this section we will investigate application of the operators in quantum physics. An operator is defined as a rulet hat transform a given function into another function. For example a differential operator transform a function in to its derivative . We are dealing linear operators which satisfy the following two properties: (A is an operator) where A is operator, f and g are functions and c are constant. Now let us introduce basic properties of operators. Basic Properties of Operators Most of the properties of operators are obvious, but they are summarized below for completeness. The sum and difference of two operators and are given by The product of two operators is defined by Two operators are equal if for all functions The identity operator does nothing (or multiplies by 1) The associative law holds for operators The commutative law does not generally hold for operators. In general, . It is convenient to define the quantity which is called the commutator of and . Note that the order matters, so that If and commute then . The
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This note was uploaded on 01/12/2012 for the course CHEM 133 taught by Professor Staff during the Spring '08 term at UCSD.

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68111133-3-3-operatorsandcommutators - Operators...

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