UW Physics


Physics 545 Introduction to atomic structure

fall semester 2019

T,Th  8:00-9:15 in 2223 Chamberlin,

Office hours: TBD, or by appointment, or just stop by. 

Final Exam Wednesday Dec. 18 7:45 - 9:45 am in 2223 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 in the astronomy library.

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

Syllabus (subject to change) (updated 2019.12.10)

week lecture   date topic

reading in atomic notes

recommended reading in Woodgate HW out HW due
1 1 Th Sept 5 Introduction, Bohr model, atomic units, start Schr. equation for H atom ch.1      
2 2 T Sept 10 Schr. Eq., H atom, degeneracy, orbitals, <r^k>, momentum space wavefunction   ch. 1,2 1  
  3 Th Sept 12 periodic table, quantum defects, Coulomb wavefunctions, matrix elements        
3 4 Th Sept 19 fine structure in Hydrogen ch. 2 ch. 4   1
4 5 T Sept 24 fine structure in alkalis, start angular momentum theory: addition of angular momenta, C-G coefficients appendix A ch. 9 2  
  6 W Sept 25 continue angular momentum: tensor operators,Lande projection, Wigner-Eckart theorem, reduced matrix elements in coupled basis        
  7 Th Sept 26 hyperfine structure, Lamb shift, muonic Lamb shift and size of proton        
5 8 T Oct 1 Multielectron atoms, Configurations and terms. Determinantal products, matching terms and determinantal products ch. 3 ch. 5,6,7 3  
  9 Th Oct 3 term splitting, Slater integrals. Central field approximation.       2
6 10 Th Oct 10 fine structure in LS coupling, Hunds rules. He energy levels, singlet, triplet structure, ground and excited states, direct and exchange integrals.        
  11 T Oct 15 Yb matrix element calculation, Atom-light Hamiltonian, Zeeman effect in fine structure.   ch. 8    
7 12 W Oct 16 Zeeman effect in hyperfine structure, high field Zeeman crossing, diamagnetic response, magic B field     4 3




Oct 17

Stark effect, H_E1, scalar, tensor polarizability





8 14 T Oct 22 linear Stark effect, BBR shift        
  15 W Oct23 Einstein A,B rate equations, absorption area law, Lorentzian lineshape, saturation effects, cross section and scattering rates     5 4
  16 T Oct 29 E1 Hamiltonian for oscillating field. co- and counterrotating terms. TDPT, Fermi golden rule, semiclassical B coefficient        
9 17 W Oct 30 midterm guidance       5
    Th Oct 31 midterm in class ch. 5 ch.3 6  
10 18 Th Nov 7 quantize EM field, quantum A coefficient (Wigner-Weisskopf theory). atomic lifetimes, magnetic dipole transitions,        
11 19 T

Nov 12

lifetime scaling with n, circular state lifetime. Line broadening mechanisms: radiative, Doppler, pressure, collisional, absorption spectroscopy ch. 6      
12 20 T Nov 19 Dynamic polarizability, oscillator strength, Rabi oscillations ch. 7,9   7 6
  21 Th Nov 21 density matrix theory, two-level Bloch equations, two-photon transitions, adiabatic transfer with dark states. ch.10      
13 22 T Nov 26 optical pumping, optical forces ch.12      
    Th Nov 28 Thanksgiving       7
14 23 T Dec 3 laser cooling, radiation and gradient forces     8  
  24 W Dec 4 magneto-optical trapping slides ch. 13, 14      
15 25 T Dec 10 sisyphus and Raman cooling, Ramsey spectroscopy, T2 due to a Gaussian process        
  26 W Dec 11 atomic clocks, atomic interactions and entanglement slides       8
    W Dec 18 Final or class project presentations        

Grading: HW 50%, midterm 17%, final 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 2019.10.15)

9.30 some updates to Ch.3

10.15 fixed some typos in calculation of Yb matrix elements



Notes on various topics:



Physical constants (updated 2015.09.03) if you want all the details here are the CODATA 2014 recommended values and NIST's 2018 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 (requires Java)

6j symbol calculator

Matrix solver for linear equations on the web