|King Fahd University of Petroleum and Minerals|
Department of Physics
Energy levels and wave functions of atoms and molecules; microwave, infrared, visible and UV spectroscopes; lasers and masers; LS and j j coupling; Thomas-Fermi and Hartree-Fock approximations; relativistic effects; group theoretical considerations; collisions
This course will introduce fundamental concepts and applications of quantum mechanics to the structure of atoms and molecules; perturbation and variational calculations, self-consistent fields,
multiplets, angular momenta, Thomas-Fermi model, diatomic molecules, spectral intensities..
M. Weissbluth, “Atoms and Molecules”. Academic Press (1978)
Other helpful texts:
A homework assignment will be given every week on each of the chapters covered in the text book. Solutions should hand in for grading not later than one week after completing the chapter. Problems may be set from the textbook or from the other sources.
Late Policy: Homework is due by 5 PM on the due date. If you need an extension, email me by the day before the homework is due. Extensions will be granted quite freely, but you must include: Why you need the extension, and when you will turn it in. You can have an extension of up to one week. If you do not get an extension, the policy is 50% credit up to one week late, and zero credit after that. Also, note that late homework may not be graded in a timely manner.
Three examinations are announced during classes. The exams will be closed book but with formula sheet.
Attendance will be evaluated according to the University regulations.
Homework & Tests:
This course will be your opportunity to work lots of homework problems. Usually one set for each topic (or chapter) will be assigned. The instructor’s written solutions will be passed out when the set is due. The homework turned in will be spot-graded and returned. It is each student’s responsibility to study and understand the solution.
There will be a quiz on each chapter or topic, and a final, with no exemptions. Homework and tests should look professional. All work turned in should be on good paper and be neat and easily read. Use of good, standard notation is required. The presentation will be reflected in the grade.
On the homework and tests, you are expected to show all your work. You must solve everything by hand (no calculators, no symbolic manipulators), unless specifically stated otherwise. The work must be yours alone.
On the homework, it is acceptable to discuss homework problems with others, but each student must turn in work that he did on his own. On tests, any collaboration at all is unacceptable.
The point of the excerpt is that quantum mechanics is essential for a proper description of atomic physics and there are many quantum mechanics textbooks that would serve as useful background reading for this book. The following short list includes those that the author found particularly relevant: Mandl (1992), Rae (1992) and Griffiths (1995). The book Atomic spectra by Softley (1994) provides a concise introduction to this field. The books Cohen-Tannoudji et al. (1977), Atkins (1983) and Basdevant and Dalibard (2000) are very useful for reference and contain many detailed examples of atomic physics. Angular-momentum theory is very important for dealing with complicated atomic structures, but it is beyond the intended level of this book. The classic book by Dirac (1981) still provides a very readable account of the addition of angular momenta in quantum mechanics. A more advanced treatment of atomic structure can be found in Condon and Odabasi (1980), Cowan (1981) and Sobelman (1996).
Atomic and molecular physics is the basic study of the building blocks of macroscopic matter. Atomic and molecular physics has been and still is the testing ground of astrophysics, atmospheric science and quantum mechanics. Experimental techniques developed for the study of atomic and molecular physics and the instrumentation developed have become the tools used in chemistry, biology, medicine, engineering. Some of these tools are things such as the X-ray tube, electron microscope, oscilloscope, spectrometers, LASERS.
Atomic and molecular physics are part of our way of understanding the world around us. What we see is based on the interaction of light with matter. For this reason optics plays a role in atomic and molecular physics. Lasers were developed through our understanding of atoms and molecules. Understanding of atoms and molecules has come, in large part, through the study of atomic and molecular spectra.
What is important to remember is that quantum mechanics was developed to explain observations. The experimental observations are critical. Quantum mechanics was not some imagined “theory,” but an explanation when the previous theories disagreed with observation. What we will be exploring are some of the observations (as many as we can do in class) and the explanations of these observations.
In the class I will be attempting to mix the experimental part of atomic and molecular physics in with the theoretical. The question you should be asking is how do we know? How can we figure this out?
1. To understand physics you must actively do physics. That means that you must work with the ideas and concepts involved. It means that you must participate in class and not just sit there and expect that I will tell you the answers. It means that you must come to class prepared. Saying “I am lost” is not helpful because that statement implies that you have not attempted to address your difficulties.
2. You must be prepared for class. This means you must read along in the text. I will not necessarily say “read these pages for the next class,” but you are none the less expected to read along in the text. Being prepared also means that you must do the homework on time. I recommend that it be started immediately when assigned. Homework is for you, not for me. The purpose of homework is not to keep you busy and to keep from idleness. It is to help you apply and learn. It is a learning tool.
3. You must participate. Participation means that you will be actively involved in the material at hand not talking over your activities of the weekend or yawning for lack of coffee. It means you will actively help your classmates solve problems. If your group is complete with a task, then your group should disperse to other groups and assist those groups.
4. You must bring to class a calculator, pen, pencil, paper. You must maintain a folder which contains all of the handouts and homework from class. This should be brought to every class.
5. This is not a math class. It is a physics class. What we are concerned with understanding the physics. That does require some mathematical sophistication, but it is not simply math. We must go beyond the mathematician and look at what it means. This is a question you must ask yourself constantly.
Ask yourself what constitutes an explanation. When you are asked to explain something, is an answer that simply repeats the question acceptable? Is it reasonable to explain a physical circumstance with mathematics?
Learning is not a passive process. It is an activity. To learn requires active thinking. Learning requires struggle. It requires uncertainty and doubt. In some circumstances learning requires some suffering. Learning and understanding are NOT the same as knowledge of facts. Simply because you know that the fine structure constant is 1/137, does not mean you understand it.
I. Basic quantum review (Free reading by students)
a. Wavefunctions and their meaning
b. Schrödinger’s equation and its solutions
c. Stationary states and time independence
d. Sketching wavefunctions based on potential curve
e. Square well
f. Coulombic potential
g. Angular momentum (Chapter 1 of Weissbluth)
II. Hydrogen atom (Chapter 16 and 17 of Weissbluth)
a. Schrödinger’s equation for hydrogen
b. Transition dipole moment
c. Selection rules
d. Corrections – LS coupling
e. Zeeman Effect
III. Approximations (Chapters 14 and 17 of Weissbluth)
a. Variational and time-independent perturbation (both for degenerate cases)
b. Two-electron wavefunctions
c. Pauli principle
b. Applications (Stark effect, He-atom and H+ molecule)
IV. Multielectron atom
a. Atomic terms
b. LS coupling revisited
c. Line shapes
d. Selection rules
a. A and B coefficient
b. Gain Coefficient
c. Threshold calculations
d. Saturation of Gain
e. Power output
VI. Molecules (
a. Molecular Schrödinger equation.
b. Development of the Born-Oppenheimer approximation
c. Development of Molecular notation
d. Molecular transitions – intra potential and selection rules
e. Molecular electronic transitions – extra potential