Quantum Chemistry Supplementary Subject

8 Lectures. Second Year. Michaelmas Term.

Lecture Synopsis

  1. Operators and Commutators. Postulates of quantum mechanics. Linear operators. Hermitian operators. The unit operator. Commutators. The uncertainty principle. Constants of the motion.
  2. The Harmonic Oscillator. Hamiltonian. Creation and annihilation operators. Eigenvalues and eigenstates. Matrix elements.
  3. Angular Momentum. Angular momentum operators. Commutation relations. Raising and lowering operators. Eigenvalues and eigenstates. Coupling of angular momenta.
  4. Matrix Formulation. Matrix representations. Hermitian matrices. Hamiltonian matrices. The variational method. Secular equations. Examples.

Lecture Handouts

  1. Lecture synopsis and problem set (PDF).

Bibliography

  1. P. W. Atkins, Molecular Quantum Mechanics (2nd edition, OUP, 1983).
  2. P. A. M. Dirac, The Principles of Quantum Mechanics (4th edition, OUP, 1958).