jueves, 28 de enero de 2010

Quantum Mechanics

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.


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