PHYM002 Quantum Mechanics II 2023-24
Dr A.V. Shytov
Delivery Weeks: T1:01-11
Level: 7 (NQF)
Credits: 15 NICATS / 7.5 ECTS
Enrolment: 49 students (approx)


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. 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
  2. Time-Independent Perturbation Theory
    1. Formulae for energy shifts to the first and second order
  3. Atoms in External Fields
    1. Normal and anomalous Stark effect
    2. Spin-orbit interaction, normal and anomalous Zeeman effect
  4. Few-Particle Systems
    1. Bose and Fermi particles, the Pauli principle
    2. Two-electron system: spin addition and exchange interaction
  5. 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.
  6. Molecules
    1. Heitler-London theory
    2. Structure of molecular spectra
  7. Quantum Transitions
    1. Perturbation theory
    2. Rabi oscillations
    3. Fermi's golden rule formula.
    4. The ammonia maser
    5. Rate of spontaneous emission.
  8. Quantum Scattering
    1. Born approximation.
    2. Scattering of electrons in graphene

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
3×1-hour tutorials 3 hours SLT
5×6-hour self-study packages 30 hours GIS
4×4-hour problem sets 16 hours GIS
Reading, private study and revision 79 hours GIS


Weight Form Size When ILOS assessed Feedback
0% Guided self-study 5×6-hour packages Fortnightly 1-8 Discussion in tutorials
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.


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:


Further Information

Prior Knowledge Requirements

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


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 25 hrs
GIS - guided independent study 125 hrs
PLS - placement/study abroad 0 hrs
Total 150 hrs
Summative assessment
Coursework 0%
Written exams 100%
Practical exams 0%
Total 100%


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 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 29-Sep-14