• Introduction: Breakdown of classical theory & the introduction of quantum mechanics
• Preview: An introduction to the basic postulates through a simple example in one dimension
• Basic assumptions of QM: the wave function and probability density; linear superposition of states; observables and operators; the eigenvalue equation; Hermitian operators; position momentum and energy operators; time dependence of the wave function
• Mathematical development & its physical implications: The time-independent Schrodinger equation (TISE); Dirac notation; properties of wave functions and operators; expansions in eigenfunctions; observables & expectation values; commutation relations; the uncertainty principle; probability currents; correspondence to classical mechanics
• Applications in 1-D: the infinite square well potential; density of states; parity
• Free particles: wave packets; momentum probability density; time development of wave packets
• More solutions of the 1-D TISE: boundary conditions; potential step discontinuity; reflection and transmission coefficients; finite depth square well potential; scattering states; tunneling through a square barrier.
• The linear quantum harmonic oscillator: harmonic oscillator potential; creation and destruction operators; energy eigenvalues and eigenfunctions.
• Motion in 3-D: stationary state representation of a free particle; density of states; TISE in spherical-polar coordinates; angular momentum operators; quantisation of angular momentum; ladder operators; motion in a central potential.
• The hydrogen atom.
• Spin: introduction to linear algebra; linear transformations eigenvectors and eigenvalues; spin 1/2 systems; Pauli Spin Matrices; electron in a magnetic field; addition of angular momenta.
Books:
D. J. Griffiths: Introduction to Quantum Mechanics, Prentice Hall.
N. Zettili: Quantum Mechanics, Concepts and Applications, Wiley.
R. L. Liboff: Introductory Quantum Mechanics, Fourth Edition, Addison Wesley.
J. M. Cassels: Basic Quantum Mechanics (2nd Ed), Macmillan.
P.J.E. Peebles: Quantum Mechanics, Princeton University Press.
D. Park: Introduction to the Quantum Theory (3rd Ed), McGraw-Hill.
A. Goswani: Quantum Mechanics (2nd Ed), Wm.C. Brown Publishers.
Source: http://www.phys.um.edu.mt/NOTES/PHY2140/CrsDesc-QM.doc
