[Dr. Jayandren Rasaiah] Course Offerings -- (Schedule Variable)

Principles of Quantum Chemistry:
Quantum Mechanics (CHY 475 / 575)

(3 Credit Hours)

This is an introductory undergraduate / graduate level course in quantum mechanics with applications to omputational aspects of molecular quantum chemistry.

Syllabus

• Introduction to Quantum theory: Black body radiation, Photoelectric effect, Bohr theory, de Broglie hypothesis, particle in a box, symmetry and degeneracy, the uncertainty principle
• Classical mechanics, Conservative systems, Harmonic oscillator, Angular momentum. Lagrangian and Hamiltonian dynamics, Poisson Brackets, Virial theorem, The principle of least action. Path integral formulation of quantum mechanics.
• Foundations of Quantum mechanics. Hermitian Operators, Postulates of Quantum mechanics, the Schrodinger equation, Time evolution and conservation laws, the Heisenberg picture, Hellman-Feynman theorem, the virial theorem.
• Solutions to Schrodinger equation for a particle in a box and the linear harmonic oscillator. Barrier penetration, Wave packets, the double harmonic oscillator.
• Orbital angular momentum. The Rigid rotor, Hydrogen atom, Spin angular momentum. Addition of angular momenta. Clebsch-Gordon coefficients.
• Approximation methods. Perturbation theory for degenerate and non degenerate systems. Applications.
• Time dependent perturbation theory. Fermi's Golden rule. Rabi formula
• Variation method, linear variation method. Applications.
• Hydrogen molecule ion.
• Molecular orbital theory
• Calculation of electronic structure. Hartree-Fock self consistent fields. Electron correlation. Density functional theory

Texts

• Molecular Quantum Mechanics Third edition P. W. Atkins and R. S. Friedman, Oxford
• Lecture Notes on Quantum Mechanics - J. C. Rasaiah
• Mathematics for Quantum Chemistry- Jay Martin Anderson , W.A.Benjamin
• Computational Quantum Chemistry by A. Hinchliffe: John Wiley

References

• Quantum Mechanics P.C.W. Davies and D. S. Betts, second edition Chapman and Hall
• Quantum Chemistry by D. McQuarrie University Science Books.
• Quantum Chemistry by I. Levine. Prentice Hall
• Introductory Quantum Mechanics by R. L. Liboff, Addison Wesley