Lecture 2: Fine structure, Lamb shift - University Of IllinoisLecture 2: Fine structure, Lamb shift...
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Lecture 2: Fine structure, Lamb shift Readings: Foot 1.4, 2.3 Last Time : eigenstates and energies for hydrogen-like atoms lots of energy degeneracy, only n-dependence () ( ) ϕ θ ψ , lm nl nlm Y r R = ( ) 2 2 2 2 2 1 / − = − = ∞ n Z c m hcR n Z E n α µ µ 137 1 4 0 2 ≈ = c e πε α Today : corrections to these energies due to stuff we ignored new terms will be come in at higher powers of [e.g. relativity, electron spin, QED, etc.]
Transcript of Lecture 2: Fine structure, Lamb shift - University Of IllinoisLecture 2: Fine structure, Lamb shift...
Lecture 2: Fine structure, Lamb shiftReadings: Foot 1.4, 2.3
Last Time: eigenstates and energies for hydrogen-like atomslots of energy degeneracy, only n-dependence
( ) ( )ϕθψ ,lmnlnlm YrR=
( )2
22
2
21/
−=−= ∞ n
ZcmhcRnZEn
αµµ
1371
4 0
2
≈=c
eπε
α
Today: corrections to these energies due to stuff we ignored
new terms will be come in at higher powers of 𝛼𝛼[e.g. relativity, electron spin, QED, etc.]
Relativistic effects: (1) KE correction
electrons can run very fast, and so we need to considerrelativistic corrections to their kinetic energy (p2/2m)
Relativistic effects: (1) KE correction
( ) ( ) ...2222 =−+= mcpcmcKE
Relativistic effects: (2) Darwin term
The electron actually wiggles very fast, on a short length scale(Zitterbewegung)
Effectively feels a “time-averaged” or “wiggle-averaged” potential,modifying the energy when the electron is near the nucleus
Relativistic effects: (2) Darwin term
Relativistic effects: (2) Darwin term
Relativistic effects: (2) Darwin term
Relativistic effects: (2) Darwin term
Relativistic effects: (2) Darwin term
( )rZeH wiggleDδξ
πεπ 2
0
2
42
=
Relativistic effects: (1&2)
Relativistic effects: (1&2)
Relativistic effects: (3) Spin-Orbit
EcvB
×−= 2
sg Bs µµ −=
BE ⋅−=∆ µ
wikipedia
Fine structure
2P3/2
2P1/2
nLJ
Lamb shift – interactions with the vacuumObserved energy shift between states with same J value
Also, no explanation for spontaneous emission
Lamb shift – interactions with the vacuum
Lamb shift – interactions with the vacuum
Lamb shift – interactions with the vacuum
value from Udem paper 1045.0079(72) MHz
Lamb shift – coupling to virtual phonons
Precision measurements in AMO physics
Precision measurements in AMO physics
Precision measurements in AMO physics
Quantum-limited measurements
Kasevich group, Nature 2016
Looking aheadReadings: Foot Ch.3
Next week: multi-electron atoms, and then hyperfine structure
Homework due next Friday, office hours on Wed / Thurs
