Lecture12 - Postulates of quantum mechanics Any state of a...

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1 Physical Chemistry Lecture 12 Wave Equations and States Postulates of quantum mechanics Any state of a dynamical system of N particles is described as fully as is possible by a function, , such that the quantity * d 3 r is proportional to the probability of finding r between r and r + d 3 r . For every observable property of a system, there exists a corresponding linear hermitian operator The physical properties of the observable can be inferred from the mathematical properties of its associated operator. The measurement of a physical observable gives only one of the eigenvalues corresponding to that observable. Origins of quantum mechanics Hamilton’s equation for the energy of a classical system Schroedinger’s equation for the wave function of a system with a definite energy Where is the wave function corresponding to the energy E H E H ˆ Expectation value of a property If a system is in a state with wave function, , the measured property is given by an integral Must know botb the state and the operator to find the value Expectation values of measurables are real Requirement on the wave function and operator The operator must be a hermitian operator space all dV O O ˆ *   space all space all dV O dV O * * ˆ ˆ Choosing operators Operators for various observables are found by correspondence to classical equivalents For position, the operation is
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This note was uploaded on 02/02/2012 for the course CHEM 444 taught by Professor Dybowski,c during the Fall '08 term at University of Delaware.

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Lecture12 - Postulates of quantum mechanics Any state of a...

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