UW Physics


Physics 545 Introduction to atomic structure

fall semester 2017

T,Th  1:00-2:15 in 2104 Chamberlin,

Office hours: M 9-10, T 8:30-9:30, W 9-10, or by appointment, or just stop by. 

Final Exam Monday Dec. 18 12:25 - 2:25 in 2135 Chamberlin

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

Syllabus (subject to change) (updated 2017.12.03)

week lecture   date topic

reading in atomic notes

reading in Woodgate HW out HW due
1 1 Th Sept 7 Introduction, Bohr model, atomic units, Schr. Eq., H atom        
2 2 T Sept 12 degeneracy, orbitals, <r^k>, quantum defects, Coulomb wavefunctions, matrix elements, start fine structure ch. 1 ch. 1,2 1  
  3 Th Sept 14 fine structure in H and alkalis ch. 2 ch. 4    
3 4 T Sept 19 alkali doublet anomaly, start angular momentum theory: addition of angular momenta, C-G coefficients appendix A   2 1
  5 Th Sept 21 finish angular momentum: tensor operators, Wigner-Eckart theorem, Lande projection   ch. 9    
4 6 T Sept 26 a Clebsch Gordan rule, hyperfine structure, Lamb shift ch.4   3 2
  7 Th Sept 28 muonic Lamb shift, Zeeman effect and mixing, hyperfine Zeeman        
5 8 T Oct 3 high field Zeeman crossing, diamagnetic response, magic B field, Stark effect, HE1     4 3
  9 Th Oct 5 derive scalar, tensor static polarizability, linear Stark effect, BBR shift        
6   T Oct 10 - ch.5 ch.3 5 4
  10 Th Oct 12 Einstein A,B, area law, Lorentzian lineshape, saturation, cross section        
7 11 T Oct 17 midterm review. E1 Hamiltonian for oscillating field. co- and counterrotating terms ch. 6     5
    Th Oct 19 Midterm in class        
8 12 T Oct 24 TDPT, Fermi golden rule, semiclassical B coefficient, quantize EM field ch. 3   6  
  13 Th Oct 26 Midterm solutions. quantum A coefficient, atomic lifetimes.        


T Oct 31 line broadening mechanisms: radiative, Doppler, pressure, collisional, absorption spectroscopy ch. 7   7 6
  15 Th Nov 2 Continuum states and photoionization - simple model, ch. 8, 9      
10 16 T Nov 7 Photoionization in high energy limit. Dynamic polarizability. Oscillator strengths. ch. 3 ch. 5 8 7
  17 Th Nov 9 Multielectron atoms, He energy levels, singlet, triplet structure   ch. 6, 7    
11 18 T

Nov 14

He ground and excited state perturbation theory, direct and exchange integrals, N-electron allowed terms,   ch. 8 9 8
  19 Th Nov 16 determinantal products, matching terms and determinantal products, term splitting, Slater integrals        
12 20 T Nov 21 LS coupling fine structure, Hund's rules ch. 10     9
    Th Nov 23 Thanksgiving        
13 21 T Nov 28 Zeeman effect in LS coupling, CFA, Hartree method, Rabi oscillations     10  
  22 Th Nov 30 density matrix theory, two-level Bloch equations ch.11      
14 23 T Dec 5 two-photon transitions, dark states, optical pumping, optical forces ch.12   11 10
  24 Th Dec 7 laser cooling, magneto-optical trap, sisyphus and Raman cooling (briefly) ch. 13, 14      
15 25 T Dec 12 optical traps, atomic coherence, atomic clocks, entangled atoms       11
    M Dec 18 Presentation of class projects 12:25 - 2:25        

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 2017.12.12)

9.12: added some material to chapter 1

9.14: added material to sec. 1.8.1, minor changes to Ch. 2

9.19: minor updates to Ch. 1,2

9.21: corrected typos

9.21: Ch. 2 - minor edits of hyperfine interaction presentation

9.28: Ch. 4 - edits to Zeeman interaction

10.03: Ch. 14 added section on atomic clocks

10.12: Ch. 5 - minor edits

10.15: Ch. 5 - added material on microscopic refractive index, FRG material moved to Ch. 6

10.26: Ch. 6 - minor edits

10.30: Ch. 6 - fixed minus sign in M1 decay rate. Some rewording for clarity.

11.09: Ch. 3 - partial version

11.14: Ch. 3 - He atom

11.16, 21,24, 28: Ch.3 material on configurations and terms added

11.30: fixed some typos

12.04 updated ch.13

12.11 updated ch.14 section on atomic clocks


Notes on various topics:



Physical constants (updated 2013.09.03) 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)

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:

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