Study information

# Quantum Mechanics II - 2023 entry

MODULE TITLE CREDIT VALUE Quantum Mechanics II 15 PHYM002 Unknown
DURATION: TERM 1 2 3
DURATION: WEEKS 11
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.

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 Guided Independent Study 25 125
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled learning & teaching activities 20 hours 20×1-hour lectures Scheduled learning & teaching activities 2 hours 2×1-hour problems/revision classes Scheduled learning & teaching activities 3 hours 3×1-hour tutorials Guided independent study 30 hours 5×6-hour self-study packages Guided independent study 16 hours 4×4-hour problem sets Guided independent study 79 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
Guided self-study (0%) 5×6-hour packages (fortnightly) 1-8 Discussion in class
4 × Problems sets (0%) 4 hours per set (fortnightly) 1-8
Solutions discussed in problems classes.

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 0 100
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 (January) 1-8 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%) 1-8 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:

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 Eisberg, R.M. and R. Resnick Quantum Physics of Atoms Molecules Solids Nuclei and Particles Wiley 1974 0-471-23464-8
Extended McMurry, S.M. Quantum Mechanics Addison-Wesley 1994 0-201-54439-3
Extended Open University Science Foundation Course Team Quantum Mechanics: An introduction Open University 1988
Extended Open University SM355 Course Team Quantum Mechanics: Units 12-14 Open University 1986
Extended Open University SM355 Course Team Quantum Mechanics: Units 15-16 Open University 1986
Extended Park, D. Introduction to the Quantum Theory 2nd edition McGraw-Hill 1974
Extended Pauling, L. and E. B. Wilson Introduction to Quantum Mechanics McGraw-Hill 1935
CREDIT VALUE ECTS VALUE 15 7.5
PRE-REQUISITE MODULES PHY2022, PHY2025
NQF LEVEL (FHEQ) AVAILABLE AS DISTANCE LEARNING 7 No Thursday 15th December 2011 Thursday 26th January 2023
KEY WORDS SEARCH Physics; Dirac notation; Energy; Eigenvalues; Eigenstates; Helium Atom; Observables; Particles; Perturbation theory; Quantum mechanics; Schrödinger equation; Scattering theory; Time; Waves.