Week 1: Failures of Classical Mechanics, Black Body Radiation, Photoelectric effect, Specific heat of monoatomic solids, Line spectra of a Hydrogen atom and Bohr’s Model, Compton shift, Heisenberg uncertainty Principle, de-Broglie’s wave-particle duality, Schrodinger equation.
Week 2: Postulates of quantum mechanics: wave function, Operators, Eigenvalue equation
Week 3: Postulates of quantum mechanics: Expectation value, Time-dependent Schrodinger wave equation. Particle in a one-dimensional box. The average value of position and momentum. 2-D box and three-dimensional box.
Week 4: Simple Harmonic Oscillator, Ladder Operator method and Power series method
Week 5: Rigid Rotor, Separation of variables, Solution phi-equation and theta equations, Legendre Equation, Associated Legendre Polynomials
Week 6: Hydrogen atom, Solution of Radial Equation, Associated Laguerre Polynomial, Radial wave function, Radial distribution function
Week 7: Concept of angular momentum, Commutators of Angular Momentum Operator, Ladder Operators, Eiegen values of total orbital angular momentum and z-component of angular momentum
Week 8: Russel-Saunder’s term and spin-orbit coupling scheme, term separation energies for the pn and dn configuration, Approximation methods in Quantum mechanics, and Variation methods applied to the one-dimensional box and hydrogen atom.
Week 9: Perturbation theory, First order Perturbation to eigenvalue and eigenfunctions for non-degenerate systems, Degenerate Perturbation theory and time-dependent perturbation theory.
Week 10: Valence Bond Theory, Hybridization sp sp2 and sp3 hybridization.
Week 11: Molecular Orbital Theory H2+-molecule ions and secular determinants, Diatomic molecules, HMO approximation for Ethylene, Allyl system, Cyclopropenyl system and Butadiene
Week 12: HMO approximation of Butadiene, Cyclobutadiene, and Benzene. Quantum mechanics in nano-scale materials, a summary of the course.
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