Basic Properties of Operators

Basic Properties of Operators - • The associative law...

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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 (33) (34) The product of two operators is defined by (35) Two operators are equal if (36) for all functions . The identity operator does nothing (or multiplies by 1) (37) A common mathematical trick is to write this operator as a sum over a complete set of states (more on this later). (38)
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Unformatted text preview: • The associative law holds for operators (39) • • The commutative law does not generally hold for operators. In general, . It is convenient to define the quantity (40) • • which is called the commutator of and . Note that the order matters, so that . If and happen to commute, then . • The n-th power of an operator is defined as successive applications of the operator, e.g. (41) • • The exponential of an operator is defined via the power series (42)...
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This note was uploaded on 11/22/2011 for the course CHEMISTRY CHM1025 taught by Professor Laurachoudry during the Fall '10 term at Broward College.

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Basic Properties of Operators - • The associative law...

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