Quantum Mechanics

Pre requisite- 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.

Theory of Wave motion: Classical Waves and Wave equation, stationary waves and nodes, Schrodinger equation, wave function and its physical meaning, condition of normalisation and orthogonality, quantum mechanical operators, Eigen values and Eigen functions, basic postulates of quantum mechanics.

Application of Schrodinger equation to-

Free particle and particle-in-a-box (rigorous treatment), one-dimensional box, quantization of energy levels, zero-point energy and justification for Heisenberg uncertainty principle; Extension to two and three dimensional boxes, degeneracy, wave functions, probability distribution functions, nodal properties.

Simple harmonic oscillator model of vibrational motion: Classical treatment, quantum mechanical treatment: Setting up of Schrodinger equation and discussion of solution and wavefunctions, comparison of classical and quantum mechanical results.

Rigid rotator model of rotation of diatomic molecule.

Schrodinger equation, transformation tospherical 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⁺. Calculation of Energy levels from wave functions, Physical picture of bonding and antibonding wave functions. Qualitative extension to H₂. Comparison of LCAO-MO and VB treatments of H₂ (only wavefunctions, detailed solution not required) and their limitations. Hybrid orbitals- sp, sp², sp³, calculation of coefficients of AO’s used in these hybrid orbitals.

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).

Polarization– Dipole moment, Induced dipole moment, dipole moment and structure of molecules, Clausius-Mossotti equation.

An overview of computational chemistry, molecular mechanics, electronic structure method, semi-empirical, ab initio and density functional methods, principle of model chemistry, desirable features of a model chemistry.