Physics H190, Spring 2001

Problems and Solutions in Atomic and Optical Physics and Related Field

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When and where: Wednesdays, 4:10-5:40 p.m., room 329 LeConte

Instructor: Assistant Professor D. Budker. Office: 219 Birge, Labs: B225, 217, 221, 230,241,245 Birge, tel. 643-1829, e-mail:, research group web page:

Office hour: Tu, 1-2, 219 Birge.

Format: one 1.5 hr class meeting per week (student participation strongly encouraged), homework

Synopsis and goals of the course
The course will be devoted to solving a variety of physics problems. Wherever possible and appropriate, we will try to use, in place of a formal mathematical solution, approximate methods, such as dimensioanal analysis, perturbation theory, etc. Some of the topics we might cover in the problems include:

1. Estimates, estimates… Estimation techniques, units, orders of magnitude, statistics, common sense problems.
2. Simple atoms. Hydrogen, hydrogenic ions, Geonium, hydrogen-like atoms (muonium etc.), fine and hyperfine structure, Zeeman and Stark Effects, atomic polarization.
3. Multi-electron atoms. Helium, the periodic table, lanthanides and actinides, Hund's rules, configurations and terms, Thomas-Fermi model, isotope shifts and hyperfine structure.
 4. Simple molecules. Electronic, vibrational and rotational levels, quantum statistics and molecular levels, hyperfine structure and isotope shifts, molecular dipole moments.
5. Atoms, molecules and light. Emission, absorption, scattering, resonance fluorescence, collective effects, Hanle and Faraday effects.
6. Experimental methods. Optical pumping, magnetic resonance, Ramsey's method, atomic beams, high-resolution laser spectroscopy, quantum beats, laser cooling and trapping, light-induced drift, Bose-Einstein Condensation, nonlinear magneto- and electro-optics, fundamental symmetry tests.
7. Lasers, optics, quanta. Optical resonators and interferometers, physics of various types of lasers, QED, cavity QED, nonlinear optics.
8. Atomic Nuclei. Atomic physics methods in nuclear physics, cold and ultra-cold neutrons, laser-driven fusion.

Our approach to posing and solving the problems is based on the desire that the problem contains at least one "memorable" physics idea, and would admit an elegant solution, not requiring elaborate mathematics. We hear from students to whom we offered many of these problems in other classes, that they are frequently amazed by unexpected physical insights that can be gained from solving these seemingly straightforward problems.

Some textbooks that may be used in conjunction with this course include:
a. S. Svanberg. Atomic and Molecular Spectroscopy. Springer-Verlag, Berlin, Heidelberg, New York, 1992..
b. H. Haken and H. C. Wolf. The Physics of Atoms and Quanta. Springer-Verlag, 1993.
c. B. H. Bransden and C. J. Joachain. Physics of Atoms and Molecules. Longman, 1988.
d. I. I. Sobelman. Atomic Spectra and Radiative Transitions. Springer, 1992.
e. S. Stenholm. Foundations of Laser Spectroscopy. Wiley, 1984.
f. N. V. Karlov. Lectures on Quantum Electronics. Boca Raton, Fla. : CRC Press, c1993.
g.  O. Svelto. Principles of Lasers. Plenum, 1989.
h. L. D. Landau and E. M. Lifshits. Quantum Mechanics.
i. N. F. Ramsey. Molecular Beams. Oxford, 1990.
j. W. Demtr der. Laser Spectroscopy. Springer, 1996.
k. I. B. Khriplovich. Parity Nonconservation in Atomic Phenomena. Gordon&Breach, 1991.
l. I. B. Khriplovich and S. K. Lamoreaux, CP violation without strangeness : electric dipole moments of particles, atoms, and molecules. New York : Springer-Verlag, c1997.
m. W. H. King. Isotope Shifts in Atomic Spectra. Plenum, 1984.
n. H. A. Bethe and E. A. Salpeter. Quantum Mechanics of One- and Two-electron Atoms. Plenum 1977.
o. A. R. Edmonds. Angular momentum in quantum mechanics. Princeton University Press, 1974.
p. R. N. Zare, Angular momentum : understanding spatial aspects in chemistry and physics. New York : Wiley, c1988.
q. D. Suter. The physics of laser-atom interactions. Cambridge University Press, 1997.
r. A. Corney. Atomic and Laser Spectroscopy. Oxford, 1979.
s. P. F. Bernath. Spectra of Atoms and Molecules. Oxford University Press, New York, Oxford, 1995.
t. D. J. C. Jones. Atomic Physics. Chapman&Hall, London, 1997.
u. Y. R. Shen. The Principles of Nonlinear Optics. Wiley.
v. A. Siegman. Lasers. University Science Books, c1986.
w. A. Yariv. Quantum Electronics. Wiley.
x. A. Yariv and P. Yeh. Optical Waves in Crystals. Wiley.
y. R. Loudon. The quantum theory of light. 2nd ed. Oxford : Clarendon Press ; New York, Oxford University Press, 1983.
z. L. D. Landau and E.M. Lifshitz. Electrodynamics of continuous media. Pergamon.
aa. R. W. Boyd. Nonlinear optics. Boston : Academic Press, c1992.
bb. H. J. Metcalf and P. van der Straten. Laser cooling and trapping. Springer, 1999.
cc. K. S. Krane. Introductory nuclear physics. New York : Wiley, c1987. xiii, 845 p.

Newsflash! Sumposium in honor of Professor E. D. Commins (May 20-21, 2001)
Find out about the 2000Nobel Prizes in Physics
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Seminars and Colloquia

Physics 290 F "Atomic" Seminar
LBNL Nuclear Science Division Colloquia
Physics Department Colloquia, Seminars, and Special Events

Lecture Notes, Electronic Tutorials

MathematicaTM notebook: Particle in an infinite square well                              Download MathReader from 
An HTML version of the above
MathematicaTM notebook: Two-level quantum mechanical system with periodic perturbation - elementary tutorial
Solidification pipes: from solder pots to igneous rocks
Dark states (J=1->J=0 transition)
Two- and three-level systems and all that
Laser cooling: some very basic ideas

Useful Links, Web Resources

Physics137A: Quantum Mechanics
Physics124: Introductory Nuclear Physics
Physics 250: Selected hot, cool, and ultracold topics in modern atomic physics
LBNL Table of Isotopes and related links
Glossary of Nuclear Terms
Web Elements Periodic Table
Nuclear Science Division, LBNL
Particle Data Group (PDG)
Radioactivity and radiation protection (from PDG)
Some links that may help you with mathematics
Spherical Bessel functions


Assignment 1 (due March 21)
Consider the interaction of light of wavelength l with small spherical metal particles of radius a<< l. Estimate the power absorbed by the particle per unit time. To solve this problem, devise a simple model that captures the essential physical mechanism leading to heating. Discuss the dependence of the absorbed power on the particle size and on the light frequency. Make numerical estimates for the case of silver particles with a=0.3 mm, l=1.06 mm (Nd-YAG laser), and a light pulse with total power 1 J, beam cross-section 1 cm2, and pulse duration of 10 ns. How hot will the particle be at the end of the pulse? Will it be intact?
Assignment 2 (due April 17)
In this problem, we analyze losses in power transmission lines. Although, at first glance, this subject appears quite unrelated to Atomic, Molecular, and Optical (AMO) Physics, as we have seen again and again throughout the semester, all physics is really the same. I promise that this problem will give us valuable AMO insights.
a) Describe a high-power transmission line. Estimate (or find in the literature, or on the web) voltage, current, and the diameter of the wires. Why does the line operate at 60 Hz AC? What determines the distance between wires?
b) "Serious" high-power lines usually have 6 wires. Explain why this is so, and comment on the relative location of the wires.
c) What are the main power-loss mechanisms? Estimate the losses per unit length (in W/m) for a 3-wire and a 6-wire line.

Acknowledgment and Disclaimer: This material is based in part upon work supported by the National Science Foundation under Grant No. PHY-9733479. Any opinions, findings and conclusions or recomendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation (NSF).