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Indian Institute of Science Education and Research Bhopal


CHM 642: Principles of Quantum Chemistry (4)

Prerequisites: MTH 101, PHY 101, CHM 101, MTH 102, PHY 102, MTH 201, PHY 201 or their equivalent Not allowed for Physics majors

Review of basic concepts of quantum theory: wave-particle duality and de Broglie wavelengths, uncertainty principle, superposition and state of a quantum system.

Mathematical background: Operators in quantum mechanics and their properties, eigenvalues and eigenfunctions, commutation relations, unitary transformations and change of basis. Matrix representation of operators.

Postulates of quantum mechanics: States and wavefunctions, observables and the measurement hypothesis, Born interpretation of wavefunction, time evolution of states and the Schrodinger equation, stationary states, compatible observables and the generalized uncertainty principle.

One-dimensional problems: Particle in a well and transmission through a barrier. Probability currents and the equation of continuity. Two and three-dimensional potential wells and degeneracy. Applications to conjugated molecules and other one-dimensional systems. Linear harmonic oscillator – ladder operator method, parity of harmonic oscillator eigenfunctions. Rigid rotor problem, angular momentum, angular momentum eigenvalues and eigenfunctions.

The hydrogen atom: Atomic orbitals – radial and angular wavefunctions and distributions, electron-spin and spin operators. Virial theorem and application to hydrogen atom and other problems. Hydrogen-like atoms.

Atoms in external fields: Zeeman and Stark effect.

Approximation methods: Time-independent perturbation theory – Anharmonic oscillator, He atom, H2+ molecular ion. Variational theorem - He atom, H2+ molecule and the LCAO approach.

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