# Atomic and Molecular Physics (PHYS*4120)

**Code and section:** PHYS*4120*01

**Term:** Fall 2011

**Instructor:** Robert Brooks

## Details

## 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).

### Course Materials

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 | ALEX 028 |

### Course Content

#### Part 1 Atoms (65%)

- 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.

#### Part 2 Molecules (35%)

- Electronic Structure

Born-Oppenheimer Separation, variational solution of H2+ 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.

### Course 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.

### 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

- Doubly-excited states of helium
- Hyperfine interactions in atoms
- Lamb shift of atomic hydrogen
- Determination of elemental abundances in stars
- Trapping of single particle; e.g. Penning trap
- Multiphoton ionization
- Quantum chaos
- Third harmonic generation (non-linear laser spectroscopy)
- Spectroscopy of excimers - He2 and HeH
- Interstellar molecules
- Spectroscopy of comets
- Matrix isolation spectroscopy
- Photoionization of atoms, ions or molecules
- Photodetachment
- Density matrix
- Celestial masers
- Laser cooling of atoms
- Atom lasers
- Negative ions
- C60 - Fullerenes
- Magnetic moment of the electron
- Muonic atoms
- Rydberg atoms
- Accurate two-electron calculations
- Slow light
- The Lyman forest
- Rabi oscillations
- Making anti-hydrogen

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 25**

Term Paper Marking Considerations

- Grammar/Syntax/Spelling 20 pts.
- 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 - Organization 10 pts.

Are topic headings or chapters used and are they meaningful? - Content 30 pts.

Appropriate level and use of mathematics

Originality of idea and/or execution

Accuracy

Appropriate use of figures - Clarity 10 pts.

Are explanations easy to understand or is the material needlessly difficult? - Coherence 10 pts.

Does it all come together or is it a collection of disjoint paragraphs/sections, etc.? - 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

## Course Policies

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.