Quantum Mechanics

Black-body radiation, Planck’s radiation law, photoelectric effect, heat capacity of solids; Bohr’s model of hydrogen atom (no derivation) and its defects, Compton effect, de Broglie hypothesis, Heisenberg’s uncertainty principle.

Postulates of quantum mechanics, quantum mechanical operators, Schrodinger equation and its application to free particle and particle-in-a-box (rigorous treatment), quantization of energy levels, zero-point energy and Heisenberg Uncertainty principle; wavefunctions, probability distribution functions, nodal properties, Extension to two and three dimensional boxes, separation of variables, degeneracy. Qualitative treatment of simple harmonic oscillator model of vibrational motion: Setting up of Schrodinger equation and discussion of solution and wavefunctions.

Rigid rotator model of rotation of diatomic molecule. Schrodinger equation, transformation to spherical polar coordinates. Separation of variables. Qualitative treatment of hydrogen atom and hydrogen-like ions: setting up of Schrodinger equation in spherical polar coordinates, radial part, quantization of energy (only final energy expression), radial distribution functions of 1s, 2s, 2p, 3s, 3p and 3d orbitals and polar plots of their shapes.

Covalent bonding, valence bond and molecular orbital approaches, LCAO- MO treatment of H₂⁺. Bonding and antibonding orbitals. Qualitative extension to H₂. Comparison of LCAO-MO and VB treatments of H₂ (only wavefunctions, detailed solution not required) and their limitations. Qualitative description of LCAO-MO treatment of homonuclear and heteronuclear diatomic molecules (HF, LiH).. Qualitative MO theory and its application to AH₂ type molecules. Simple Huckel  Molecular Orbital (HMO) theory and its application to simple polyenes (ethene, butadiene).

Optical activity, polarization – Clausius-Mossotti equation, orientation of dipoles in an electric field, dipole moment, induced dipole moment, measurement of dipole moment temperature method and refractivity method, dipole moment and structure of molecules.