Lect1_hbari - Lecture 1: Demystifying h and i We are often...

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Lecture 1: Demystifying h and i •We are often told that the presence of h distinguishes quantum from classical theories. •One of the striking features of Schrödinger's equation is the fact that the variable, ! , is complex, whereas classical theories deal with real variables QM: CM: d dt x ( t ) = " p H ( x , p ) d dt p ( t ) = # x H ( x , p ) d dt v E ( v r , t ) = 1 c 2 v " # v B ( v r , t ) d dt v B ( v r , t ) = $ v " # v E ( v r , t ) •Q: Is h necessary at all? •By changing units we can of course make h disappear from QM •But if it is truly fundamental, shouldn’t this same choice of units make h appear then in CM? •If system has natural length scale and energy scale, then h is needed to relate then to the natural mass scale. i t # ( $ , t ) = % 1 2 m 0 m ( ) * + 2 "$ 2 ( , t ) + u ( ) ( , t )
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•What happens to CM in these units? •Same mass scale makes CM dimensionless as
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This note was uploaded on 12/21/2011 for the course PHY 851 taught by Professor Moore,m during the Fall '08 term at Michigan State University.

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Lect1_hbari - Lecture 1: Demystifying h and i We are often...

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