||Quantum Mechanics II
||Dr A.V. Shytov
||15 NICATS / 7.5 ECTS
||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.
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:
Module Specific Skills and Knowledge:
- formulate, and evaluate, the solutions to a variety of perturbed
quantum mechanical systems;
- calculate energy shifts, transition probabilities
(and rates) and cross-sections;
Discipline Specific Skills and Knowledge:
- use matrix concepts to solve QM problems;
- use mathematics to solve problems;
- present and defend their solutions to problems to the group;
Personal and Key Transferable / Employment Skills and Knowledge:
- undertake co-operative learning by discussing the contents of the module
- make informal presentations of technical material;
- work independently in order to meet deadlines.
Heisenberg's Approach to Quantum Mechanics
- Matrix elements for a quantum harmonic oscillator and a quantum rotor
- Electron spin and Pauli matrices
- Quantum particle in a double-well potential as a two-level system
Time-Independent Perturbation Theory
- Formulae for energy shifts to the first and second order
Atoms in External Fields
- Normal and anomalous Stark effect
- Spin-orbit interaction, normal and anomalous Zeeman effect
- Bose and Fermi particles, the Pauli principle
- Two-electron system: spin addition and exchange interaction
Structure of Many-Electron Atoms
- Electron shells
- Hund's rules,
- The role of spin-orbit interaction
- LS coupling scheme.
- Zeeman effect in many-electron atoms
- Hyperfine structure of atomic spectra.
- Heitler-London theory
- Structure of molecular spectra
- Perturbation theory
- Rabi oscillations
- Fermi's golden rule formula.
- The ammonia maser
- Rate of spontaneous emission.
- Born approximation.
- Scattering of electrons in graphene
Learning and Teaching
Learning Activities and Teaching Methods
|2×1-hour problems/revision classes
|5×6-hour self-study packages
|4×4-hour problem sets
|Reading, private study and revision
||Discussion in tutorials
||4 × Problems sets
||4 hours per set
||Solutions discussed in problems classes.
||2 hours 30 minutes
||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).
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)
Prior Knowledge Requirements
||Quantum Mechanics I (PHY2022) and Mathematics with Physical Applications (PHY2025)
Re-assessment is not available except when required by referral or deferral.
|Original form of assessment
||Form of re-assessment
||Time scale for re-assessment
||Written examination (100%)
||August/September assessment period
Notes: See Physics Assessment Conventions.
KIS Data Summary
|Learning activities and teaching methods|
|SLT - scheduled learning & teaching activities
|GIS - guided independent study
|PLS - placement/study abroad
|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
||Physics; Dirac notation; Energy; Eigenvalues; Eigenstates; Helium Atom; Observables; Particles;
Perturbation theory; Quantum mechanics; Schrödinger equation; Scattering theory; Time; Waves.