Ch01 Newtonian mechanics

In the classical limit the results obtained with

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Unformatted text preview: se. In the classical limit, the results obtained with quantum mechanics are identical to the results obtained with classical mechanics. This fact is known as the correspondence principle. In classical or newtonian mechanics the instantaneous state of a particle with mass m is fully described by the particle’s position [x(t), y(t), z(t)] and its momentum [px(t), py(t), pz(t)]. For the sake of simplicity, we consider a particle whose motion is restricted to the x-axis of a cartesian coordinate system. The position and momentum of the particle are then described by x(t) and p(t) = px(t). The momentum p(t) is related to the particle’s velocity v(t) by p(t) = m v(t) = m [dx(t) / dt] . It is desirable to know not only the instantaneous state-variables x(t) and p(t), but also their functional evolution with time. Newton’s first and second law enable us to determine this functional dependence. Newton’s first law states that the momentum is a constant, if there are no forces acting on t...
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This note was uploaded on 02/05/2013 for the course CHEM 131A taught by Professor Rentzepis during the Fall '12 term at UC Irvine.

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