From Physlab.lums.edu.pk

Instructor: Dr. [Sabieh Anwar] *Office hours:* Tuesday, Thursday (5-6 pm)

Teaching Assistant: [Shahid Sattar] *Office hours:* Tuesday, Thursday (4-6 pm)

Textbook: *Molecular Quantum Mechanics, Fourth edition* by Peter Atkins, Ronald Friedman

Course outline: Click here

**Week 1** *Spins in magnetic fields*

- Zeeman and singlet-triplet bases and their inter-conversion
- Spin in an external magnetic field, magnetogyric ratio
- Zeeman Hamiltonian
- Bloch sphere and evolution of states on the sphere

**Week 2** *Spins in magnetic fields (continued)*

- Rotation operators, viewing a propagator as a rotation operator
- evolution of observables
- rotating wave approximation
- NMR and ESR spectra

**Week 3** *Transitions between energy levels*

- Time-dependent perturbation theory basics: constant, exponentially increasing and oscillatory Hamiltonians
- Approximate and exact formulas
- Rabi flopping
- rotating wave approximation revisited
- Comparison between constant and oscillatory Hamiltonians

**Week 4** *Interaction of electric dipoles with Radiation*

- Transitions to continuum states
- Fermi golden rule
- Electric dipole interacting with an electromagnetic wave
- Absorption, stimulated and spontaneous emission
- Interaction with thermal radiation
- Einstein's A and B coefficients

**Week 5** *Lifetimes of states*

- Natural broadening
- Pressure broadening
- Doppler broadening
- Lorentzian and Gaussian lineshapes, lineshape function, homogeneous and heterogeneous broadening
- What about lineshapes in solids?
- Emission rates for a quantum harmonic oscillator and comparison with a classic accelerating electric dipole

**Week 6** *Selection rules*

- Selection rules for the magnetic quantum number

**Week 7** *Selection rules (contd.)*

- Selection rules for the orbital quantum number
- Laporte rule: electric dipole transitions are allowed between opposite parity states
- Examples of applications of selection rules
- Grotrian diagram
- Metastable states and phosphorescence
- 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)**

**Week 7 and 8** *Atomic Spectrum of hydrogen: fine structure*

- 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
- Fine structure of the H spectrum, multiplets in the Lyman and Balmer series
- Lamb shift and Lamb's experiment
**Review article for self-study:**Stern-Gerlach Experiment How a bad Cigar helped Reorient Atomic Physics

**Week 9** *Zeeman and hyperfine effects*

- The Zeeman effect: weak and strong fields
- Effect on the spectrum by placing the atom in external magnetic field
- Hyperfine interaction
- The 21 cm line and some of its uses in radio-astronomy
- The F quantum number

**Week 10** *Multi-electron atoms (before the spin-orbit interaction)*

- Pauli's exclusion principle, fermions and bosons
- Why does the singlet electron state has a higher energy than the triplet electron state?
- Effect of Coulombic repulsion on He levels: ground and first excited state
- Hartree's theory and its important results
- Concept of effective nuclear charge

**Week 11** *The Periodic Table*

- The Periodic Table and ground state electronic configurations
- Electronic configurations and anomalies
- Why does energy depend on l?
- Trends in the periodic table explicable from Hartree's calculations
- Guest lecture by Rafiullah: Bose-Einstein condensation

**Review article for self-study:** Bose-Einstein condensation (**Source: Physicsworld.com**)

Observation of Bose-Einstein Condensation
in a Dilute Atomic Vapor (**Science, Vol 269, 1995**)

**Week 12** *Spectroscopy of Multi-electron Atoms*

- Electronic configurations, terms, levels and states
- Hund's rules
- Examples of atomic spectra: helium, alkali metals (lithium, sodium etc), alkaline earth (calcium etc)
- Atomic absorption spectroscopy
- X-ray spectroscopy
- Photoelectron spectroscopy: X-ray Fluorescence and Auger electron spectroscopy
- Zeeman effect in multi-electron systems

**Week 13** *Lasers*

- Review of spontaneous emission, stimulated emission and absorption
- Population inversion and conditions for laser operation
- Gain of the laser medium, laser as an amplifier
- laser as an oscillator
- Single and multi mode operation
- Pulsed mode operation: Q-switching and mode-locking
- Characteristics of laser light
- Some example lasers: He-Ne, excimer, Nd:YAG and diode lasers