Syllabus

Module 1: (10 hours)
Review of the atomic structure of the hydrogen atom, quantum numbers, selection rules, fine structure, and Lamb shift. Atomic structure of two-electron systems, helium atom, and exchange interactions. Alkali system, screening effects, and relativistic corrections. Electron configurations and terms, Pauli exclusion principle, and term symbols for many-electron atoms. Equivalent and nonequivalent electrons, coupling schemes, and fine structure splitting. Hund's rules and determination of ground state terms for multi-electron atoms.

Module 2: (10 hours)
Symmetric and antisymmetric wave functions, Pauli principle, and application to many-electron atoms. Slater determinants, derivation and significance in atomic systems. Constant field approximation and perturbation techniques. Hartree-Fock method, self-consistent field (SCF) approach, and applications. Vector atom model, angular momentum coupling, and multiplet structure. LS and jj coupling schemes, selection rules, and transitions. Normal and Anomalous Zeeman effects, magnetic interactions, and energy level splitting in external fields. Stark effect, electric field-induced splitting, and applications in atomic physics.

Module 3: (6 hours)
Born-Oppenheimer approximation, separation of electronic and nuclear motion in molecular systems. Spectra of diatomic molecules: rotational spectra, selection rules, and molecular parameters. Vibrational spectra, harmonic and anharmonic oscillations, selection rules, and isotope effects.

Module 4: (6 hours)
Polyatomic molecules, normal modes of vibration, symmetry, and group theory applications. Electronic spectra of molecules, potential energy curves, Franck-Condon principle, and dissociation energy. Raman effect, classical and quantum mechanical treatment, selection rules, and applications in material characterization.

Module 5: (4 hours)
Electron Spin Resonance (ESR) spectroscopy, principles and applications. Nuclear Magnetic Resonance (NMR) spectroscopy, basic principles and chemical shift. LASER principles, population inversion, and basic applications in spectroscopy. Modern experimental tools of spectroscopy, a brief overview of interferometry and Fourier-transform spectroscopy.

Understanding of atomic spectra, molecular structure, and principles of spin resonance spectroscopy (ESR and NMR).

Analyzing models of helium and multi-electron atoms, their electronic spectra, and distinguishing various angular momentum coupling schemes and their consequences.

Applying the Franck-Condon principle to analyze electronic, rotational, and vibrational spectra of diatomic molecules, along with the fundamentals of IR spectroscopy.

Exploring models of polyatomic molecules to explain electronic, vibrational, and rotational levels, and applying classical and quantum theory of the Raman effect.

5. Learning the principles and applications of modern spectroscopic techniques, including LASER, interferometry, and Fourier-transform spectroscopy.

At the end of the course, students will be able to:
CO1: Describe the atomic spectra of one- and two-valence-electron atoms, including fine and hyperfine structure.

CO2: Analyze the behavior of atoms in external electric and magnetic fields, explaining the Stark and Zeeman effects.

CO3: Explain the rotational, vibrational, electronic, and Raman spectra of diatomic and polyatomic molecules.

CO4: Describe the principles and applications of electron spin resonance (ESR) and nuclear magnetic resonance (NMR) spectroscopy.

CO5: Apply theoretical concepts to understand modern spectroscopic techniques, including LASER and Fourier-transform spectroscopy.

C. N. Banwell and E. M. McCash, Fundamentals of Molecular Spectroscopy, Tata-McGraw Hill (2007).

B. H. Bransden and C. J. Joachain, Physics of Atoms and Molecules, Prentice Hall (2003).

G. Herzberg, Molecular Spectra and Molecular Structure: I. Spectra of Diatomic Molecules, Krieger Publishing Company (1989).

H. Haken and H. C. Wolf, The Physics of Atoms and Quanta: Introduction to Experiments and Theory, Springer (2005).