Study information

Quantum Mechanics I - 2024 entry

MODULE TITLEQuantum Mechanics I CREDIT VALUE15
MODULE CODEPHY2022 MODULE CONVENERDr Claire Davies (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 5
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 profoundly affects the way we think about the universe and is the basis for much of condensed-matter, nuclear and statistical physics, and physical chemistry. 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 and PHYM002 Quantum Mechanics II. 

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

 

Introduction  

What is required of a theory of quantum mechanics; time-dependent Schrödinger equation; Born probability interpretation of the wave function; normalisation of the wave function; first postulate; Gaussian wave packets.  

 

 
Stationary States and the Time-Independent Schrödinger Equation  

Time-independent probability distributions; the time-independent Schrödinger equation; stationary states: eigenfunctions of the Hamiltonian; commutation with the Hamiltonian; momentum eigenfunctions in 3D; Schrödinger equation in 3D Cartesian coordinates; Schrödinger equation in spherical polar coordinates; degenerate states  

  

One-dimensional problems  

The wave function of a free particle; boundary conditions; wave function of a confined particle; infinite and finite square well solutions; probability flux; continuity equation; persistence of normalisation; the potential step; reflection and transmission by a barrier; quantum tunnelling; the quantum harmonic oscillator (Schrödinger approach).  
    
Time-evolution 

The Ehrenfest theorem; uncertainty principle; Heisenberg picture; Heisenberg equation 

  

Angular Momentum  

Cartesian representation of angular momentum operators; commutation relations; polar representation of angular momentum operators; eigenfunctions and eigenvalues; rotational energy levels of a diatomic molecule; superposition principle; integer and half-integer angular momenta; addition of angular momenta; spin  

  
Centrally-symmetric potentials: The Hydrogen Atom  

Solutions of the angular equation; solutions of the radial equation; energy eigenvalues - the hydrogen spectrum; electron density distributions  

  

Identical quantum particles  

Pauli principle; Bosons-Fermions quantum statistics  

  
First-Order Time-Independent Perturbation Theory  

Anharmonic effects; Stark and Zeeman effects; Paramagnetism; Ferromagnetism 

 

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 25 Guided Independent Study 125 Placement / Study Abroad 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning & teaching activities 20 20×1-hour lectures
Scheduled learning & teaching activities 5 Problems class support
Guided independent study 30 5×6-hour self-study packages
Guided independent study 8 4×2-hour problems sets
Guided independent study 83 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 module lead  5×2-hour sets (typical)  1-12 Solutions released to ELE 
Guided self-study 5×6-hour packages 1-12 Discussion in tutorials

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 10 Written Exams 90 Practical Exams 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
4 × Problems sets 10 2 hours per set 1-12 Marked automatically by e-assessment system, with feedback provided 
Mid-term test 15 30 minutes 1-11 Marked, then collective feedback provided in class
Examination 75 2 hours 1-11 Mark, 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
All above  Written examination (100%) 1-11 Referral/Deferral period

 

RE-ASSESSMENT NOTES

Deferral – if you have been deferred for any assessment you will be expected to submit the relevant assessment. The mark given for a re-assessment taken as a result of deferral will not be capped and will be treated as it would be if it were your first attempt at the assessment. 

  

Referral – if you have failed the module overall (i.e. a final overall module mark of less than 40%) you will be expected to submit the relevant assessment. The mark given for a re-assessment taken as a result of referral will be capped at 40% 

 

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

The following list is offered as an indication of the type & level of information that students are expected to consult. Further guidance will be provided by the Module Instructor(s). 

 
Core text: 

  •  
    Rae A.I.M. & Napolitano J. (2016), Quantum Mechanics (6th Edition), CRC Press, ISBN 9781138458338 
     

Supplementary texts: 

  •  
    McMurry S.M. (1994), Quantum Mechanics, Addison Wesley, ISBN 0-201-54439-3 (UL: 530.12 MCM) 

 

Reading list for this module:

There are currently no reading list entries found for this module.

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 Tuesday 1st October 2024
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.