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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 singleparticle 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) 
David Sherrill
20060815