UW Physics


Physics 545 Introduction to atomic structure

fall semester 2018

T,Th  8:00-9:15 in 2120 Chamberlin,

Office hours: M 1:30-2:30, W 9:00-10:00, or by appointment, or just stop by. 

Final Exam Thursday Dec. 20 7:45 - 9:45 am in Chamberlin 2135

Mark Saffman
Department of Physics
office: 5330 Chamberlin
tlf: 265 5601
email: msaffman@wisc.edu
web: hexagon.physics.wisc.edu

Course catalog description: Nuclear atom; hydrogen atom; Bohr-Sommerfeld model, wave model, electron spin, description of quantum electron spin, description of quantum electrodynamic effects; external fields; many-electron atoms; central field, Pauli principle, multiplets, periodic table, x-ray spectra, vector coupling, systematics of ground states; nuclear effects in atomic spectra. Prerequisites: A course in quantum mechanics or cons inst.Course listing in UW timetable.

The recommended (not required) supplementary textbook is G. K. Woodgate, Elementary atomic structure, Oxford

Several alternative texts are available on course reserves.

books on atomic physics(notes and other materials are only available on the UW computer network)

Syllabus (subject to change) (updated 2018.11.27)

week lecture   date topic

reading in atomic notes

recommended reading in Woodgate HW out HW due
1 1 Th Sept 6 Introduction, Bohr model, atomic units ch.1      
2 2 T Sept 11 Schr. Eq., H atom, degeneracy, orbitals, <r^k>, momentum space wavefunction   ch. 1,2 1  
  3 Th Sept 13 periodic table, quantum defects, Coulomb wavefunctions, matrix elements        
3 4 T Sept 18 fine structure in Hydrogen ch. 2 ch. 4 2 1
  5 Th Sept 20

fine structure in alkalis, alkali doublet anomaly, start angular momentum theory: addition of angular momenta, C-G coefficients

appendix A ch. 9    
4 6 T Sept 25 continue angular momentum: tensor operators,Lande projection        
  7 Th Sept 27 Wigner-Eckart theorem        
5 8 T Oct 2 Lande projection theorem, reduced matrix elements in coupled basis, strength of H 1s-2p transitions. start hyperfine structure ch. 3 ch. 5,6,7   2
  9 Th Oct 4 hyperfine structure, Lamb shift, muonic Lamb shift and size of proton. Start multielectron atoms.     3  
6 10 T Oct 9 Multielectron atoms, Configurations and terms. Determinantal products, matching terms and determinantal products        
  11 Th Oct 11 term splitting, Slater integrals. Central field approximation. He energy levels, singlet, triplet structure He ground and excited state perturbation theory, direct and exchange integrals,   ch. 8    
7 12 T Oct 16 fine structure in LS coupling, Hunds rules. Zeeman effect        




Oct 18

Zeeman effect in fine and hyperfine structure, high field Zeeman crossing, diamagnetic response





8 14 T Oct 23 magic B field, Stark effect, HE1, derive scalar, tensor static polarizability        
  15 Th Oct 25 review, linear Stark effect, BBR shift       4
9   T Oct 30 midterm in class        
  16 Th Nov 1 midterm solutions, Einstein A,B rate equations ch. 5 ch.3    
10 17 T Nov 6 absorption area law, Lorentzian lineshape, saturation effects, cross section and scattering rates. E1 Hamiltonian for oscillating field. co- and counterrotating terms     5  
  18 Th Nov 8 TDPT, Fermi golden rule, semiclassical B coefficient, quantize EM field, quantum A coefficient (Wigner-Weisskopf theory)        
11 19 T

Nov 13

atomic lifetimes: magnetic dipole transitions, scaling with n, circular state lifetime. Introduction to using atoms as qubits. ch. 6      
  20 Th Nov 15 line broadening mechanisms: radiative, Doppler, pressure, collisional, absorption spectroscopy ch. 7      
12 21 T Nov 20 Dynamic polarizability. Oscillator strengths, Rabi oscillations ch. 9     5
    Th Nov 22 Thanksgiving        
13 22 T Nov 27 density matrix theory, two-level Bloch equations, two-photon transitions, adiabatic transfer with dark states. ch.10   6  
  23 Th Nov 29 optical pumping, optical forces ch.11      
14 24 T Dec 4 atomic clocks (guest lecture Prof. Kolkowitz) slides ch. 12   7 6
  25 Th Dec 6 laser cooling, magneto-optical trap, sisyphus and Raman cooling (briefly) ch. 13, 14      
15 26 T Dec 11 optical traps, atomic coherence, entangled atoms slides       7
    M Dec 17 Written class projects due by 5 pm        
    Th Dec 20 Presentation of class projects 7:45-9:45 am        

Grading: HW 50%, midterm 17%, final project 33%


Homework is an important part of the course and accounts for 50% of your grade. Working problems is an integral part of learning physics, and will also give you practice in applying mathematical methods. You are encouraged to use the math resources provided in the notes and links below.

Homework will typically be given out on a tuesday and due the following tuesday. You are welcome to work together on homework, however you must turn in your own solutions - not a Xerox copy of someone else's. Late homework will not be accepted unless prior approval has been given. Assignments and solutions will be provided by email.

Atomic notes:

atomic notes (updated 2018.11.27)

9.19 corrected minor typos, added material on fine structure and proton radius in ch. 2

10.09 reorganized ch.3 and added new material

10.15 ch.4 - corrected lower/upper case labeling

10.25 corrected some minor typos

11.27 corrected some minor typos



Notes on various topics:



Physical constants (updated 2015.09.03) if you want all the details here are the CODATA 2010 recommended values and NIST's 2014 updates.

Conversion between Gaussian and SI units (v1.2, 2009.01.20)

Quantum mechanics primer (updated 2016.09.27)

A little bit of quantum information

Time independent perturbation theory

Time dependent perturbation theory

Mathematical formulae (updated 2017.09.28)

Special relativity notes (version 1.2, updated 2008.02.17) A good introduction to special relativity that is much more detailed than my notes can be found here.

Tutorial on Fourier transforms Note that this tutorial uses a different convention than us. The prefactor in one-dimension is 1/(2pi) for the inverse transform (k->x) and just 1 for the forward transform (x->k). We are using a symmetric form where the prefactor is 1/sqrt(2 pi) in each direction.

Some interesting papers related to the course:


Einstein photoelectric effect (1905)

Einstein special relativity (1905)

Einstein radiation theory (1917)

Einstein and quantum theory (review 1979)

H matrix elements:

Gordon matrix elements (1929)


H Fine structure, hyperfine structure, and Lamb shift:

Hydrogen data (2010)

Lamb original measurement (1947)

Series of six papers by Lamb, et al. giving more experimental and theoretical details (1950-1953)


Welton's Lamb shift calculation (1948)

Newer calculations (1967)

Newer experiments (1979)

Cs microwave clock:

NIST F1 accuracy (2002)


Absorption in atomic vapors:

Rb D lines, Hughes, Adams (2008)

Rb saturated absorption spectroscopy, Freegarde (2010)

Purcell effect:

Purcell effect(1946)

Haroche observation of enhanced decay (1983)

Kleppner theory of inhibited decay (1981)

Kleppner observation of inhibited decay (1985)


Space quantization (1937)

Magnetic resonance note (1938)

Molecular beam magnetic resonance method (1939)

Laser cooling:

Adams laser cooling review (1997)

Letokhov laser cooling and trapping review (2000)

Metcalf laser cooling review (2003)

subDoppler cooling of Na (1988)



Atomic parity nonconservation:

Bouchiat derivation of relevant weak interaction (1974)

Bouchiat review of parity nonconservation (1997)

JILA experiment (1997)

JILA experiment - all the details (1999)

Links to useful information:

Periodic table

NIST Physical reference data

NIST Atomic Spectroscopy reference

Harvard CFA databases

Wikipedia - atomic physics

Physics World

Math World

Wolfram function site

Digital library of mathematical functions

Abramowitz & Stegun Handbook of Mathematical Functions

Integrals on the web

Clebsch-Gordan calculator

6j symbol calculator

Matrix solver for linear equations on the web