Faculty of Science

Objectives

To compliment the first part of Quantum mechanics, and lay a strong foundation for the undergraduate level.

Contents

General Structure of Quantum Mechanics, Eigenfunctions and expansion theory, Analogy with vector spaces, Linear operators, Hermitian operators, Completeness, degeneracy, Complete sets of commuting observables, Uncertainty relations, The classical limit of quantum theory; Operator Methods in Quantum Mechanics: The harmonic operation problem, Raising and lowering operators, Eigenstates and eigenvalues, the interpretation as probability amplitude, The time development of a system in terms of operator, the Schroedinger and Heisenberg pictures; Angular Momentum: Central potentials, Commutation relations for angular momentum, representation of angular momentum operators in polar coordinates, Spherical Harmonics, Matrix representation of operators, Applications, The Hydrogen Atom: The Schroedinger equation for the hydrogen atom, exact solution of the Schrodinger equation. N Particle System: The Schroedinger equation for N Particle Systems, Momentum and Conservation, Reduced mass, the Pauli principles, Fermions and Bosons in a box, the Fermi energy; Approximate Methods: Time independent perturbation, Second order perturbed energy, Applications of perturbation theory, Time dependent perturbation, Spontaneous and induced emission.