- General
- Aims and Objectives
- Syllabus
- Coursework
- Computing and Tools
- Schedule
- Deadlines
- Marking Scheme
- Experiments
- Lecture Notes
Welcome to the Quantum Mechanics A (PHY-319 QMA) Home Page
The module organiser is Dr Theo Kreouzis, the deputy is Prof Andreas Brandhuber
This is a first (semi) formal course in Quantum mechanics; students enrolling on PHY-319 must have completed Quantum Physics (QP | PHY-215) or equivalent.
The assessment for PHY-319 is as follows:
Weekly problem sheets 10%
Mid-term test (50 minutes) 10% 2011 mid-term for practice purposes
Final examination (two and a half hours) 80% 2011 exam paper for revision purposes
2011 exam paper solutions for revision purposes
Please use the tabs (above) to access specific information and links to files.
IMPORTANT NOTICE: The mid-term test will take place at 12:00 on Tuesday the 26th of February 2013
Office hours: I will be available on Thursdays from 12:00 to 14:00 (in my office) to answer student questions, give advice etc.
Text book: B.H. Bransden and C.J. Joachain, Quantum Mechanics, Pearson/Prentice Hall, ISBN 978-0-582-35691-7
Aims and Learning Outcomes
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.
Learning 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.
Exercises
There are weekly problem sheets to be solved and handed in by Thursday at 16:00. The actual problems can be found in the coursework tab.
In addition to these, excercise class questions are solved during the classes in order to gain practice. You will be allocated one of three Friday exercise classes during your first week of lectures.
Syllabus
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.
Coursework
This module has weekly problem sheets to be solved independently and handed in for marking, as well as weekly excercise classes where questions are solved during the class. The problem sheets are attached as below, and the exercise class questions are to be found on page two of the sheets.
problems 1
problems 2
problems 3
problems 4
problems 5
problems 6
problems 7
problems 8
exercise class prolems 9
Useful files
I have attached a useful Excel graph plotter. It is set to plot two trivial functions and the difference between them; feel free to edit it in order to solve numerical problems.
I also attach a simple bit of mathematica code using the FindRoot function; again, feel free to edit and use...
STM data : QMA-STM-I-z.txt
| Week | Dates | A1 | A2 | A4 | A4 |
|---|---|---|---|---|---|
| Monday | Tuesday | Thursday | Friday | ||
| 1 | Introduction and postulates | ||||
| 2 | The infinite square well, conjugated oligomers | ||||
| 3 | The finite square well | ||||
| 4 | The harmonic oscillator | ||||
| 5 | Probability currents | ||||
| 6 | Quantum Mechanical Tunnelling | ||||
| Reading week | |||||
| 8 | Mid-term test and the STM | ||||
| 9 | The Hydrogen atom | ||||
| 10 | The Hydrogen atom (continued) and angular momentum | ||||
| 11 | Perturbation Theory | ||||
| 12 | Revision/past paper practice | ||||
Deadlines
The deadline for weekly coursework submission is 16:00 on Thursday. Any work submitted after this must be accompanied by an extenuating circumstances form!
Marking
The problems sheets are returned marked by the first Thursday after submission. Please check the first floor pigeon holes for marked work, also, marked scripts may be returned during the Friday exercise classes.
Model answers will appear as pdf files (linked below), ususally by the first Monday after the submission deadline for any individual problem set.
solutions 1
solutions 2
solutions 3
solutions 4
solutions 5
solutions 6
solutions 7
solutions 8
Experiments
There are two experimental demonstrations as part of this course.
Absorption spectra of conjugated oligomers
The absorption spectra for different conjugated oligomers can be found by clicking on the links below.
NB:
I have saved these as tab delimited (.txt) files that ought to be readable irrespective of software used.
The first column is the photon wavelength in nm and the second column the absorption coefficient
The Scanning Tunnelling Microscope (STM)
STM notes
STM data: QMA-STM-I-z.txt
I have linked a selection of summary notes in pdf format that are useful for this course. Please note that, although numerous, these notes are not a complete set of my lecture notes and miss out many of the mathematical steps carried out in detail during my lectures. The presence of these online notes is no substitute for lecture attendance! They are best printed out beforehand and annotated by the student during the lectures.