# Atomic and Molecular Physics (PHYS*4120)

Code and section: PHYS*4120*01

Term: Fall 2009

Instructor: Robert Brooks

## Course Information

### Objectives

The student will learn to apply the principles of quantum mechanics to a variety of situations in atomic and molecular physics, mostly of bound states (structure).

### Textbook

Bound notes available for sale (abt \$15) in SCIE1101A first week of class. After that in the main office. (MacN 207.)

### Lectures

Day Time Location
Tu Th 10:00-11:20 MACN 118

### Course Topics

Topics Specifics
Central Forces and Angular Momentum Commutator relations, ladder operators, review of the hydrogen-atom solution, spherical harmonics, spin angular momentum, addition of angular momentum.
Complex Atoms Antisymmetrization and Slater determinants, angular momentum for complex atoms, matrix elements of the Hamiltonian including derivations of the Coulomb and Exchange Integrals, Slater sum rule, energies of the three lowest terms of carbon as example. Hartree-Fock equations (brief) and discussion of correlation energies.
Electro- and Magnetostatic Interactions Static perturbations including fine structure, Stark effect and Zeeman effect.
Transition Probabilities Time dependent perturbation theory, Fermi's golden rule, lifetimes of excited states, transition selection rules.
Electronic Structure Born-Oppenheimer Separation, variational solution of $H_2^{+}$ using prolate spheroidal coordinates and evaluation of all integral expressions; analogous solution for H2 without integral evaluations; systematics and symmetries of first row diatomic molecules.
Vibrations and Rotations of Diatomic Molecules Separation of coordinates, harmonic and anharmonic vibrations, simple rotations, Morse potential, interpretation of spectroscopic molecular constants, transition selection rules, thermal distributions, spin statistics.

### Evaluation

Assessment Weight
Problem Assignments 20%
Term Paper 20%
Midterm Exam 25%
Final Exam 35%

Medical Certificate: Required if the midterm or final exams are missed.
Consultation: Free to see me at any time. Tuesdays and Thursdays after class are best. Otherwise send an E-mail to make a simple appointment. Not around Mondays and most Fridays.

### Student "Cooperation"

Students may discuss problems among themselves but the written solutions must be primarily the work of the student who submits it. Under no circumstances must the written solution be shared with anyone. Term papers must be entirely the work of the student submitting it with any copied material put in quotation marks with references.

### References

• Quantum Theory of Matter (2nd ed.)
John C. Slater
McGraw Hill (1968)
• Molecular Spectra and Molecular Structure
Vol I: Spectra of Diatomic Molecules (2nd ed.)
Gerhard Herzberg
Van Nostrand Reinhold (1950)
• Quantum States of Atoms Molecules and Solids
Morrison, Estle and Lane
Prentice-Hall (1976)
• Angular Momentum in Quantum Mechanics
A.R. Edmonds
Princeton University Press (1974)
• Atomic Spectra and Atomic Structure
Gerhard Herzberg
Dover
• Intermediate Quantum Mechanics (2nd ed.; or later)
H.A. Bethe and R.W. Jackiw
Benjamin (1968)
• Principles of Modern Physics
Robert B. Leighton
McGraw-Hill (1959)
• Principles of Atomic Spectra
Shore and Menzel
John Wiley and Sons (1968)
• Atomic and Quantum Physics
H. Haken and H.C. Wolf
Springer-Verlag (1987)
• The Hartree-Fock Method for Atoms (advanced)
Charlotte Froese Fischer
John Wiley (1977)

### Suggested Term Paper Topics

1. Doubly-excited states of helium
2. Hyperfine interactions in atoms
3. Lamb shift of atomic hydrogen
4. Determination of elemental abundances in stars
5. Trapping of single particle; e.g. Penning trap
6. Multiphoton ionization
7. Quantum chaos
8. Third harmonic generation (non-linear laser spectroscopy)
9. Spectroscopy of excimers - He2 and HeH
10. Interstellar molecules
11. Spectroscopy of comets
12. Matrix isolation spectroscopy
13. Photoionization of atoms, ions or molecules
14. Photodetachment
15. Density matrix
16. Celestial masers
17. Laser cooling of atoms
18. Atom lasers
19. Negative ions
20. C60 - Fullerenes
21. Magnetic moment of the electron
22. Muonic atoms
23. Rydberg atoms
24. Accurate two-electron calculations
25. Slow light
26. The Lyman forest
27. Rabi oscillations

A topic selected by the student not on this list is OK if approved by instructor before the 12th class day.

Hint: The series Advances in Atomic and Molecular Physics in the library offers many good review articles

Term papers shall be 2 to 3 thousand words, typewritten, double spaced. Creation of your own figures or tables is encouraged but don’t cut and paste figures and tables from other’s work. It is not permitted for scientific papers and this is a practice for such writing. Any words or phrases taken verbatim from any source must be surrounded in quotes with the reference stated. Avoid web sources that are not refereed publications.

Term papers are due: End of Week 11 - November 27

Term Paper Marking Considerations

1. Grammar/Syntax/Spelling 20 pts.
2. Fidelity to original intent 10 pts.
Ability to step back and take a larger view of some subject relevant to A&M; not to get overly specific or to be highly mathematical
3. Organization 10 pts.
Are topic headings or chapters used and are they meaningful?
4. Content 30 pts.
Appropriate level and use of mathematics
Originality of idea and/or execution
Accuracy
Appropriate use of figures
5. Clarity 10 pts.
Are explanations easy to understand or is the material needlessly difficult?
6. Coherence 10 pts.
Does it all come together or is it a collection of disjoint paragraphs/sections, etc.?
7. References 10 pts.
Appropriate number and kind for the subject matter.
Web refs are permitted but don’t count. They are not refereed in any way