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Study information

Quantum Mechanics I - 2023 entry

MODULE TITLEQuantum Mechanics I CREDIT VALUE15
MODULE CODEPHY2022 MODULE CONVENERDr Claire Davies (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11
Number of Students Taking Module (anticipated) 170
DESCRIPTION - summary of the module content

This module introduces the mathematical expression of the basic principles of quantum mechanics and methods for finding solutions of problems that permit straightforward mathematical analysis. These solutions demonstrate many of the general features of the subject and will be applied in subsequent modules in the Physics programme.

AIMS - intentions of the module
Quantum Mechanics is one of the fundamental building-blocks of Physics. It affects profoundly the way we think about the universe and is the basis for much of condensed-matter, nuclear and statistical physics. It also has a strong influence on technological developments, for instance in optical and electronic devices. This module aims to give students a firm grounding in the subject and to prepare them for future modules such as PHY3052 Nuclear and High-Energy Particle Physics.
 
INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)
A student who has passed this module should be able to:
 
Module Specific Skills and Knowledge:
1. describe the definition and interpretation of the wavefunction and of operators in quantum mechanics;
2. discuss the origin of energy quantisation and quantum tunnelling effects;
3. describe the general properties of the stationary states of quantum particles confined to simple symmetric potentials;
4. perform calculations on wavefunctions, and solve the Schrödinger equation for a range of problems;
5. use time-independent perturbation theory to solve problems and interpret results;
6. explain the origin of the un-coupled set of quantum numbers for the hydrogen atom and the form of the associated eigenfunctions;
 
Discipline Specific Skills and Knowledge:
7. use the principles of quantum mechanics to solve problems;
8. explain quantum mechanics to a lay-person in an informed manner;
 
Personal and Key Transferable / Employment Skills and Knowledge:
9. construct arguments that explain observations;
10. solve problems by using mathematics;
11. use a range of resources to develop an understanding of topics through independent study.
12. meet deadlines for completion of work for problems classes and develop appropriate time-management strategies.
 
SYLLABUS PLAN - summary of the structure and academic content of the module
I. Introduction
Brief historical survey; recap of PHY1022; what is required of the theory; the wave equation; time-dependent Schrödinger equation
II. Wave Functions and their Interpretation
The Born probability interpretation; normalization of the wave function; first postulate; wave function of a free particle; wave function of a confined particle; Gaussian wave packets (Self-study pack): the uncertainty principle; time evolution of wave packets
III. Dynamical Variables
Observables as operators; the second postulate; the third postulate; physical significance of eigenfunctions; Schrödinger equation revisited
IV. Stationary States and the Time-Independent Schrödinger Equation
Time-independent probability distributions; the time-independent Schrödinger equation; stationary states: eigenfunctions of the Hamiltonian; example: region of constant potential; method of solution ; boundary conditions
V. Particle in a Box - the Infinite Square Well
Internal solution; boundary conditions; energy quantization; normalized wave functions
VI. The Finite Square Potential Well (Self-study pack)
Interior and exterior solutions; boundary conditions; symmetric solutions - energies and wave functions; antisymmetric solutions - energies and wave functions
VII. Flow of Particles
Probability flux; continuity equation; persistence of normalization; derivation of probability flux
VIII. Barrier Problems
Boundary conditions at a potential discontinuity; a potential step; tunnelling: reflection and transmission by a barrier; practical examples of tunnelling
IX. Quantum Measurement and the Structure of Quantum Mechanics
Properties of Hermitian operators; the superposition principle: fourth postulate; measurements of a general quantum state; commutation relations and simultaneous observables; the uncertainty principle; commutation with the Hamiltonian; summary: the postulates of quantum mechanics
X. The Quantum Harmonic Oscillator
Hamiltonian in operator form; ladder operators; eigenvalues and eigenfunctions
XI. The 3D Time-Independent Schrödinger Equation
Momentum eigenfunctions in 3D; Schrödinger equation in 3D Cartesian coordinates (Self-study pack); example: particle in a 3D box; Schrödinger equation in spherical polar coordinates
XII. Angular Momentum
Cartesian representation of angular momentum operators; commutation relations; polar representation of angular momentum operators; eigenfunctions and eigenvalues; example: Rotational energy levels of a diatomic molecule
XIII. The Hydrogen Atom
Solutions of the angular equation; solutions of the radial equation; energy eigenvalues - the hydrogen spectrum; electron density distributions
XIV. First-Order Time-Independent Perturbation Theory
Perturbation theory for non-degenerate levels; perturbation theory for degenerate levels
LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 33 Guided Independent Study 117 Placement / Study Abroad
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning & teaching activities 22 hours 22×1-hour lectures
Guided independent study 30 hours 5×6-hour self-study packages
Guided independent study 16 hours 8×2-hour problems sets
Scheduled learning & teaching activities 8 hours Problems class suppor
Scheduled learning & teaching activities 3 hours Tutorial support
Guided independent study 71 hours Reading, private study and revision

 

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Exercises set by tutor (0%) 3×1-hour sets (typical) (Scheduled by tutor) 1-12 Discussion in tutorials
Guided self-study (0%) 5×6-hour packages (Fortnightly) 1-12 Discussion in tutorials
       
       
       

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 10 Written Exams 90 Practical Exams
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
8 × Problems sets 10% 2 hours per set (Weekly) 1-12 Marked in problems class, then discussed in tutorials
Mid-term test 15% 30 minutes (Term 1, Week 6) 1-11 Marked, then discussed in tutorials
Examination 75% 120 minutes (January) 1-11 Mark via MyExeter, collective feedback via ELE and solutions.
         
         

 

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-assessment
Whole module Written examination (100%) 1-11 August/September assessment period

Re-assessment is not available except when required by referral or deferral.

RE-ASSESSMENT NOTES
An original assessment that is based on both examination and coursework, tests, etc., is considered as a single element for the purpose of referral; i.e., the referred mark is based on the referred examination only, discounting all previous marks. In the event that the mark for a referred assessment is lower than that of the original assessment, the original higher mark will be retained.
 
Physics Modules with PHY Codes
Referred examinations will only be available in PHY3064, PHYM004 and those other modules for which the original assessment includes an examination component - this information is given in individual module descriptors.
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener
ELE:
 

Reading list for this module:

Type Author Title Edition Publisher Year ISBN
Set Rae, A.I.M. Quantum Mechanics 5th edition Chapman and Hall 2007 1-584-88970-5
Extended McMurry, S.M. Quantum Mechanics Addison-Wesley 1994 0-201-54439-3
CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES PHY1026
CO-REQUISITE MODULES
NQF LEVEL (FHEQ) 5 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Thursday 15th December 2011 LAST REVISION DATE Thursday 26th January 2023
KEY WORDS SEARCH Physics; Energy; Eigenvalues; Eigenstates; Hydrogen Atom; Observables; Particles; Perturbation theory; Quantum mechanics; Schrödinger equation; Time; Waves.

Please note that all modules are subject to change, please get in touch if you have any questions about this module.