Module Description
PHYM002 Quantum Mechanics II 2013-14
Dr A.V. Shytov
 
Delivery Weeks: T1:01-11
Level: 7 (NQF)
Credits: 15 NICATS / 7.5 ECTS
Enrolment: 48 students (approx)

Description

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.

Module Aims

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)

A student who has passed this module should be able to:

Syllabus Plan

  1. Dirac Notation
  2. Non-degenerate Perturbation Theory
    1. Introduction
    2. Mathematical basis
    3. Perturbation method
    4. Sequence of perturbation equations
    5. Solution of first-order equation
    6. First-order result for change to energies and wavefunctions
    7. Second-order energy shifts
    8. Anharmonic oscillator
    9. Finite-nucleus correction
  3. Degenerate Perturbation Theory
    1. Introduction
    2. "Almost degenerate" limit of nondegenerate perturbation theory
    3. Solution of the problem of a doubly degenerate state
    4. Stark effect
  4. Quantum Transitions
    1. Introduction
    2. Time-dependent perturbation theory
    3. First-order theory
    4. Constant perturbation from t = 0
    5. Energy conservation
    6. Transition rate, Fermi's golden rule
    7. Harmonic perturbation and induced energy changes to a quantum system
  5. Two-particle Systems
    1. Noninteracting particles
    2. Helium atom
    3. Exchange interaction
    4. Spin eigenvalues and eigenfunctions for two electrons
    5. Spin wave functions and interchange symmetry
    6. Hydrogen molecule
  6. Many-particle Systems
  7. Nonrelativistic scattering theory
    1. Incident and scattered waves
    2. Integral equation
    3. Scattering amplitude
    4. Phase shifts
    5. Differential cross section
    6. Total cross section
    7. Born approximation
  8. Introduction to quantum information

Learning and Teaching

Learning Activities and Teaching Methods

Description Study time KIS type
20×1-hour lectures 20 hours SLT
2×1-hour problems/revision classes 2 hours SLT
5×6-hour self-study packages 30 hours GIS
4×4-hour problem sets 16 hours GIS
Reading, private study and revision 82 hours GIS

Assessment

Weight Form Size When ILOS assessed Feedback
0% Guided self-study 5×6-hour packages Fortnightly 1-8 Discussion in class
0% 4 × Problems sets 4 hours per set Fortnightly 1-8 Solutions discussed in problems classes.
100% Final Examination 2 hours 30 minutes January 1-8 Mark via MyExeter, collective feedback via ELE and solutions.

Resources

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:

Supplementary texts:

ELE:

Further Information

Prior Knowledge Requirements

Pre-requisite Modules Quantum Mechanics I (PHY2022) and Mathematics with Physical Applications (PHY2025)
Co-requisite Modules none

Re-assessment

Re-assessment is not available except when 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

Notes: See Physics Assessment Conventions.

KIS Data Summary

Learning activities and teaching methods
SLT - scheduled learning & teaching activities 22 hrs
GIS - guided independent study 128 hrs
PLS - placement/study abroad 0 hrs
Total 150 hrs
Summative assessment
Coursework 0%
Written exams 100%
Practical exams 0%
Total 100%

Miscellaneous

IoP Accreditation Checklist
  • QM-05 Wave function and its interpretation
  • QM-06 Standard solutions and quantum numbers to the level of the hydrogen atom
  • QM-07 Tunnelling
  • QM-08 First order time independent perturbation theory
  • QM-09 Quantum structure and spectra of simple atoms
  • QM-12 Pauli exclusion principle, fermions and bosons and elementary particles
Availability MPhys and PGRS only
Distance learning NO
Keywords Physics; Dirac notation; Energy; Eigenvalues; Eigenstates; Helium Atom; Observables; Particles; Perturbation theory; Quantum mechanics; Schrödinger equation; Scattering theory; Time; Waves.
Created 01-Oct-10
Revised 11-Sep-13
Validate   Link-check © Copyright & disclaimer Share