Study information

Quantum Mechanics II - 2024 entry

MODULE TITLEQuantum Mechanics II CREDIT VALUE15
MODULE CODEPHYM002 MODULE CONVENERDr Andrey V Shytov (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11
Number of Students Taking Module (anticipated)
DESCRIPTION - summary of the module content

The module covers a range of more advanced topics leading to the discussion of quantum transitions and non-relativistic scattering. Much of physics concerns manifestations of the electromagnetic interaction which is susceptible to perturbation techniques. The methods outlined in the module are applicable to many situations in condensed matter and nuclear physics enabling useful and informative solutions to be obtained to non-exactly-soluble problems without resort to numerical methods.

Pre-requisite modules: PHY2022 and PHY2025 or equivalent modules.

AIMS - intentions of the module
The aim of this module is to build upon the foundations laid in PHY2022 Quantum Mechanics I and develop the students' grasp of quantum mechanics - particularly its formalism and applications - to the point where they will be able to engage with contemporary research literature.
 
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. formulate, and evaluate, the solutions to a variety of perturbed quantum mechanical systems;
2. calculate energy shifts, transition probabilities (and rates) and cross-sections;
 
Discipline Specific Skills and Knowledge:
3. use matrix concepts to solve QM problems;
4. use mathematics to solve problems;
5. present and defend their solutions to problems to the group;
 
Personal and Key Transferable / Employment Skills and Knowledge:
6. undertake co-operative learning by discussing the contents of the module amongst themselves;
7. make informal presentations of technical material;
8. work independently in order to meet deadlines.
SYLLABUS PLAN - summary of the structure and academic content of the module
I. Heisenberg's Approach to Quantum Mechanics
  1. Matrix elements for a quantum harmonic oscillator and a quantum rotor
  2. Electron spin and Pauli matrices
  3. Quantum particle in a double-well potential as a two-level system
II. Time-Independent Perturbation Theory
  1. Formulae for energy shifts to the first and second order
III. Atoms in External Fields
  1. Normal and anomalous Stark effect
  2. Spin-orbit interaction, normal and anomalous Zeeman effect
IV. Few-Particle Systems
  1. Bose and Fermi particles, the Pauli principle
  2. Two-electron system: spin addition and exchange interaction
V. Structure of Many-Electron Atoms
  1. Electron shells
  2. Hund's rules,
  3. The role of spin-orbit interaction
  4. LS coupling scheme.
  5. Zeeman effect in many-electron atoms
  6. Hyperfine structure of atomic spectra.
VI. Molecules
  1. Heitler-London theory
  2. Structure of molecular spectra
VII. Quantum Transitions
  1. Perturbation theory
  2. Rabi oscillations
  3. Fermi's golden rule formula.
  4. The ammonia maser
  5. Rate of spontaneous emission.
VIII. Quantum Scattering
  1. Born approximation.
  2. Scattering of electrons in graphene
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 and teaching activities 20 20×1-hour lectures
Scheduled learning and teaching activities 2 2×1-hour problems/revision classes
Scheduled learning and teaching activities 3 3×1-hour tutorials
Guided independent study 30 5×6-hour self-study packages
Guided independent study 16 4×4-hour problem sets
Guided independent study 79 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
Guided self-study 5×6-hour packages (fortnightly) 1-8 Discussion in class
4 × Problems sets 4 hours per set (fortnightly) 1-8
Solutions discussed in problems classes.

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 0 Written Exams 100 Practical Exams 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Final Examination 100 2 hours 30 minutes 1-8 Written, 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
Final Examination Written examination (100%) 1-8 Referral/deferral period

 

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
Core text:
 
Rae A.I.M. (2007), Quantum Mechanics (5th edition), Chapman and Hal, ISBN 1-584-88970-5 (UL: 530.12 RAE)
 
Supplementary texts:
 
Eisberg R.M. and Resnick R. (1974), Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles, Wiley, ISBN 0-471-23464-8 (UL: 530.12 EIS)
 
McMurry S.M. (1994), Quantum Mechanics, Addison Wesley, ISBN 0-201-54439-3 (UL: 530.12 MCM)
 
Open University Science Foundation Course Team (1988), Quantum Mechanics: An introduction, Open University (UL: 500 OPE/X)
 
Open University SM355 Course Team (1986), Quantum Mechanics: Units 12-14, Open University (UL: 530.12 OPE/X)
 
Open University SM355 Course Team (1986), Quantum Mechanics: Units 15-16, Open University (UL: 530.12 OPE/X)
 
Park D. (1974), Introduction to the Quantum Theory (2nd edition), McGraw-Hill (UL: 530.12 PAR)
 
Pauling L. and Wilson E.B. (1935), Introduction to Quantum Mechanics, McGraw-Hill (UL: 530.12 PAU)

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 PHY2022, PHY2025
CO-REQUISITE MODULES
NQF LEVEL (FHEQ) 7 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Wednesday 13th March 2024 LAST REVISION DATE Wednesday 22nd May 2024
KEY WORDS SEARCH Physics; Dirac notation; Energy; Eigenvalues; Eigenstates; Helium Atom; Observables; Particles; Perturbation theory; Quantum mechanics; Schrödinger equation; Scattering theory; Time; Waves.

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