Quantum Mechanics A (QMA | SPA5319)

Please consult QMPlus for the authoritative information on this module.

Year: 2 | Semester: A | Level: 5 | Credits: 15

Prerequisites: PHY-4217 and PHY-4215 or equivalent introductory courses in quantum physics
Lectures: 26 | Ex: 514 515 Lec: 409 511 512 (notation)
Exam: 2.5 hour written paper (80%), coursework (20%)
Practical work: 2 x 1 hours | Ancillary teaching: weekly exercises, exercise class

Course organiser: Dr Timothy Clifton | Course deputy: Dr Anthony Phillips

Synopsis:

This course aims to introduce the fundamental concepts of quantum mechanics from the beginning. By studying applications of the principles of quantum mechanics to simple systems the course will provide a foundation for understanding concepts such as energy quantisation, the uncertainty principle and quantum tunnelling, illustrating these with experimental demonstrations and other phenomena found in nature. These concepts are introduced and applied to systems of increasing (mathematical) complexity: (i)Infinite 1-D quantum wells. (ii)Finite 1-D quantum wells (introducing graphical solutions of transcendental equations). (iii)LCAO methods for modelling ions. (iv)Simple Harmonic oscillators (introducing Hermite polynomials and applying energy solutions to molecular vibrational spectra). (v)Beams of free particles, probability flux and reflection/transmission in stepwise varying potentials. (vi)Finite potential barriers and tunnelling, Tunnelling through arbitrary potential barriers (the Gamow factor), field emission and Alpha decay and tunnelling. The Scanning Tunnelling Microscope (STM). (vii)The solution to the Hydrogen atom, including separation of variables, spherical harmonics, the radial equation and electronic energy levels and the quantum numbers n, l, ml and ms and resulting degeneracy. (viii)The treatment of angular momentum in quantum mechanics, its magnitude and projection along an axis. (ix)Introduction to first order, time independent, perturbation theory.

Aims:

This is a first (semi) formal quantum mechanics course; the idea is to teach basic quantum mechanical skills, which can later be used in advanced quantum mechanics courses and other related physics.

Outcomes:

At a basic level students should: Quote the Time independent Schroedinger equation (TDSE) and Time independent Schroedinger equation (TISE) and the conditions leading from one to the other. Be familiar with the concept of a wavefunction and the Born interpretation of the wavefunction; be able to sketch wavefunctions and probability densities for simple problems. Be familiar with eigenfunctions and energy eigenstates of simple systems. Normalise wavefunctions. Be familiar with the concept of operators and resulting eigenvalue equations (specifically those relating to the energy, position and momentum). Calculate the expectation value of and observable using its related operator. Calculate the uncertainty of an observable. Be familiar with the Heisenberg uncertainty relation. Realise that quantum mechanics is based on postulates and have seen/discussed these postulates. Realise that the most general solution to a quantum mechanical system is a linear combination of eigenfunctions.

Recommended books:

B.H. Bransden and  C.J. Joachain, Quantum Mechanics, Pearson/Prentice Hall, ISBN 978-0-582-35691-7
[strongly recommended]

[course notes available]