Atomic, molecular physics and optics

The lecture will describe the basics allowing you to understand how matter worlks, starting from quantum mechanics to the principles of chemistry. It will also provide some of the foundations of optics, which as you will see is deeply connected with atoms and molecules.

The lecture builds upon both your Quantum Physics I and II, and on your knowledge of electromagnetism and waves.

Here are some general bibliographic references relevant to the course:

• Atkins and Friedman, Molecular quantum mechanics
• Walraven, Atomic physics (lecture notes from the university of Amsterdam)
• Brandsen and Joachain, Physics of atoms and molecules
  

Reminders on the hydrogen atom, spectrum and Bohr formula, shape of atomic orbitals.

Video of the lecture is available here.

Relativistic corrections to the Hydrogen spectrum, hyperfine coupling.

Video recording available here.

• Reference (complete and very advanced !) for the Dirac equation and the non-relativistic limit: Bethe and Salpeter, Quantum Mechanics of One- and Two-Electron Atoms,  Chap. I, part b, Sections 10-12

Atoms in external fields, vector operators, tensor operators, selection rules and Wigner-Eckart theorem.

Video recording of the lecture can be found here.

• Gauge invariance of the Schrödinger equation: here is the proof that I skipped in the lecture.
• Reference for details on the Wigner-Eckart theorem: Complement DX of Quantum Mechanics II, Cohen-Tannoudji, Diu and Laloë (second volume of the celebrated Cohen-Tannoudji textbook on quantum mechanics).

Wigner-Eckart theorem, and tensor operators (end). Helium atom, correlation effects, variational calculation.

Video recording of the lecture available here

Many electron atoms: central field approximation, periodic table, Hartree-Fock method

Video recording available here (apologies for the low quality of the second hour).

• for a presentation of the Hartree-Fock method, see Atkins and Friedman, Chap 7, sections 12-17
• A more thorough presentation of many-electron atoms is in Walraven, Atomic Physics, Chap 9 and 10
  

Molecules: Born-Oppenheimer approximation, H2+ molecule, bonding and antibonding states, H2 molecule, Heitler-London approximation

Video recording of the lecture available here

• The lecture largely follows Atkins and Friedman, Chap. 8, sections 1-5
• A more thorough presentation can be found in Cohen-Tannoudji, Quantum Mechanics, Complement GXI, pp. 1189-1219

Molecules: Rayleigh-Ritz variational method, diatomic molecules, sigma- and pi-bonds, hybridization, structure of molecules, Hückel model

Video recording of the lecture here.

• Relevant material in Atkins and Friedman:  Chap. 6, sections 9,10; Chap. 8, sections 6-9, 12

Light propagation, paraxial propagator, Gaussian beams, Fresnel theory of diffraction, lenses.

Video recording of the lecture is here.

• J. Goodman, Introduction to Fourier Optics, Chap 4 and 5
  

Semi-classical theory of light-matter interactions, dipole approximation, selection rules, perturbative treatment, Einstein coefficients.

Video recording is here.

References:

• G.Grynberg, A.Aspect and C. Fabre, Introduction to Quantum Optics, Section 2.1 to 2.3
  

Einstein coefficients, radiation at equilibrium. Rate equations for populations, polarization, susceptibility, attenuation and dispersion.

Video recording available here.

Molecular spectroscopy: rotational and vibrational spectroscopy of diatomic molecules, Raman spectroscopy

Video recording of the lecture available here

• The lecture largely follows Atkins and Friedman, Chap. 10, sections 1-12

Molecular spectroscopy: rotational and vibrational spectroscopy of polyatomic molecules, Franck-Condon principle, summary

Video recording of the lecture available here (sorry, part 2 of 3 need to be rerecorded)

• The lecture largely follows Atkins and Friedman, Chap. 10, sections 13-15, Chap. 11, sections 4,5
• Facultative knowledge on symmetries and group theory: Atkins and Friedman, Chap. 5

Question and Answer session will take place on the

19.06.2025 in the morning from 10:00 to 12:00 in room CE 1 101

The exam will take place on the 

02.07.2025 from 9:00 to 12:00 in rooms CE 105 - CE 106