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lecture4 - Chem 120A Fall 2010 Classical physics Classical...

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Chem 120A Classical vs. quantum descriptions of nature 09/03/10 Fall 2010 Lecture 4 Classical physics • There is no fundamental separation of system and observer in classical physics • To specify a state at time t it is enough to know the values of all physical quantities at that t • Causality : state at time t 2 uniquely determined by state at t 1 < t 2 . Example Newton’s second law is a classical equation of motion: m d 2 x dt 2 = F ( x ( t ) , dx dt ) (1) but knowing x ( t 1 ) is not sufficient to specify the state at all times (one also needs to know ˙ x ( t 1 ) ). ˙ x ( t 1 ) is related to the momentum at time t 1 : ˙ x ( t 1 ) = p ( t 1 ) m . Newton’s second law can also be written: ˙ p ( t ) = F ( x ( t ) , p ( t ) m ) (2) Hence, the state is fixed at all times if the initial conditions ( i.e. x ( t 1 ) , p ( t 1 ) ) are known. Postulates of quantum mechanics 1. A quantum state is represented by a square-integrable wavefunction ψ . ( e.g. ψ ( x ) C such that Z ψ * ( x ) ψ ( x ) dx < ). To interpret the wavefunction probabilistically (which is a very useful picture!)
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