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
	13	Th	Oct 17	Stark effect, H_E1, scalar, tensor polarizability	ch.4
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

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:

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)