From Physlab.lums.edu.pk

Instructor: Dr. [Sabieh Anwar] *Office hours:* will be announced shortly.

Teaching Fellow: [Shahid Sattar] *Office hours:* Tuesday, Thursday (11:00 am to 1:30 pm)

Textbooks: There is no single prescribed textbook. Use lecture notes and the supplementary books provided in the course outline below.

Click here for the course outline.

Here is the weblink for the same course I taught in Fall 2010.

**Spins**

- Spin spectroscopy
- Zeeman Hamiltonian
- NMR and ESR spectra
- Spin dynamics inside a magnetic field
- Bloch sphere and evolution of spin states
- Rotation operator and Rabi flopping
- Rotating wave approximation
- On-resonance and off-resonance effects
- Quadrature detection

**Suggested Reading**: Spin Dynamics by M. Levitt, Ch. 1-5

**Homework No. 1**

Spin Dynamics

HW Solution

**Interaction of radiation and matter**

- Using time-dependent perturbation theory to obtain transition rates between levels
- Concepts of: Rabi flopping, transition matrix elements, electric dipole operator, rotating wave approximation
- Fermi's golden rule
- Interaction of matter with thermal radiation and comparison with coherent Rabi oscillations
- Einsten's A and B coefficients
- Lineshapes and broadening mechanisms
- Eignefunctions of the one-electron atoms
- Quantum statistics and indistinguishability
- Bose-Einstein condensation
- Laser cooling
- Magneto optical trap (MOT)

**Suggested Reading**: Introduction to Quantum Mechanics by Griffiths, Ch. 9, Atomic Physics by C.J. Foot, Ch 7

Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles by Eisberg and Resnick, Ch. 11

**Practice questions**

Transitions between energy levels

Solutions

**Homework No. 2**

Transitions between energy levels, Due date: Oct. 29, 2011

**Homework No. 3**

Bose-Einstein condensation, Due date: Nov. 11, 2011

HW Solution

**Midterm Examination**

Question paper

Formula sheet

Solution set

**Atomic Spectroscopy: fine structure of hydrogen atom**

- Fine structure: relativistic correction
- Fine structure: spin-orbit interaction:
**Review articles for self-study:**On the classical analysis of spin-orbit coupling in hydrogenlike atoms (**Am. J. Phys. 78 (4), 2010**) The Thomas precision factor in spin-orbit interaction (**Am. J. Phys. 72 (1), 2004**) - Good quantum numbers
- The quantum number j and fine structure of the energy levels
- Selection rules for the magnetic quantum number
- Selection rules for the orbital quantum number
- Grotrian diagram
- Angular momentum and helicity of the photon:
**Review article for self-study:**A justification of selection rules Spectroscopic selection rules: The role of photon states (**J. Chem. Ed., Vol. 76 No. 9, 1999)**

**Suggested Reading**: Introduction to Quantum Mechanics by Griffiths, Section 6.3.

**Homework No. 4**

Atomic spectroscopy and fine structure of hydrogen, Due date: Nov. 23, 2011

HW Solution

**Atoms inside magnetic fields and role of nucleus in the spectrum**

- Zeeman effect: strong and weak field cases
- Using degenerate perturbation theory for intermediate magnetic fields
- Hyperfine interaction
- Here is a chart showing Clebsch-Gordan coefficients. Useful for the application of degenerate perturbation theory for determining the Zeeman shifted energy levels.
- Determination of Zeeman shifted states for n=2: PDf version of a Mathematica file. Email me to obtain the Mathematica notebook.

**Suggested Reading**: Introduction to Quantum Mechanics by Griffiths, Sections 6.4 and 6.5.

**Homework No. 5**

Zeeman effect and hyperfine interaction

HW Solution

**Molecular spectroscopy**

- Rotational spectroscopy
- Vibrational spectroscopy
- Raman scattering
- Fluorescence

**Final Examination from the year 2010 (Practice questions)**

The first four questions are relevant to this year.

Question paper

Solution set