Operators - refer to the operator acting on NH , for...

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Operators Levine [ 3 ] defines an operator as ``a rule that transforms a given function into another function'' (p. 33). The differentation operator is an example--it transforms a differentiable function into another function . 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
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Unformatted text preview: refer to the operator acting on NH , for example. Operators and Quantum Mechanics In quantum mechanics, physical observables (e.g., energy, momentum, position, etc.) are represented mathematically by operators. For instance, the operator corresponding to energy is the Hamiltonian operator (31) where is an index over all the particles of the system. We have already encountered the single-particle Hamiltonian in equation ( 25 ). The average value of an observable A represented by an operator for a quantum molecular state is given by the ``expectation value'' formula (32)...
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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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