Lect1_hbari

# 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: CE&M: 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 well ! •Q: Are Maxwell’s Eq’s ‘classical’ or ‘quantum’? •Apply De Broglie hypothesis to Einstein’s equation: •The wavefunction of a massless particle obeys the Maxwell wave equation ! •So is E just the photon wavefunction? •‘Classical’ E&M would be ‘quantum’ if the photon had

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