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Lecture16

# instantaneous power is p equaeng the classical power

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Unformatted text preview: Eon of charge. Synchrotron: Suppose we have a charged harmonic oscillator whose moEon is described as: ! d 2r 2! +! r = 0 2 dt This will emit an electromagneEc wave (light) of frequency ω 2 e2 a 2 The instantaneous power of this emission will be: P = 3 4!!0 c 3 2 e2 "4 ! 2 For harmonic moEon, a =  ­ω2r P = r 3 3 4!!0 c acceleraEon (Larmor) 12 Correspondence principle Consider a single photon emiked in Eme τ. !! Instantaneous power is P = " EquaEng the classical power with the quantum mechanical power above: 1 P 2 e2 "3 " 2 The rate: R = = = r 3 ! !" 3 4#!0 ! c Expressing the above in terms of the ﬁne structure constant: ! 2 " !2 R= ! 2 r 3c 3 ! =c/ f !2 16! r R= "f 2 3 # = e2 / ( 4"!0 !c ) 3 13 EsEmate of transiEons in hydrogen 2 "3 ! 2 TransiEon from 2p to 1s state in hydrogen: R = ! r 2 3c 2s 1s 2p !2 We can replace r 2 = a0 R a0 = ! me c! 22 E2 " E1 me c 2# 2 \$ 1 ' 3me c # != = & (" ) " ("1) ) = ! 2! % 4 8! ( 2 ! ! 2 27 me3c 6! 6 54 c 2! 5 me R= = 2 22 2 33 3 c me c ! 8! 1536 ! R = 5.66 ! 10 8 s "1 ! = 1.7 ns 14 Quantum mechanical rate First gue...
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