PHYM002 
Quantum Mechanics II 
201920 

Dr A.V. Shytov 


Delivery Weeks: 
T1:0111 

Level: 
7 (NQF) 

Credits: 
15 NICATS / 7.5 ECTS 

Enrolment: 
49 students (approx) 

Description
The module covers a range of more advanced topics leading to the discussion of
quantum transitions and nonrelativistic 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 nonexactlysoluble 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:

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 crosssections;

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 cooperative learning by discussing the contents of the module
amongst themselves;
 make informal presentations of technical material;
 work independently in order to meet deadlines.
Syllabus Plan

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 doublewell potential as a twolevel system

TimeIndependent Perturbation Theory
 Formulae for energy shifts to the first and second order

Atoms in External Fields
 Normal and anomalous Stark effect
 Spinorbit interaction, normal and anomalous Zeeman effect

FewParticle Systems
 Bose and Fermi particles, the Pauli principle
 Twoelectron system: spin addition and exchange interaction

Structure of ManyElectron Atoms
 Electron shells
 Hund's rules,
 The role of spinorbit interaction
 LS coupling scheme.
 Zeeman effect in manyelectron atoms
 Hyperfine structure of atomic spectra.

Molecules
 HeitlerLondon theory
 Structure of molecular spectra

Quantum Transitions
 Perturbation theory
 Rabi oscillations
 Fermi's golden rule formula.
 The ammonia maser
 Rate of spontaneous emission.

Quantum Scattering
 Born approximation.
 Scattering of electrons in graphene
Learning and Teaching
Learning Activities and Teaching Methods
Description 
Study time 
KIS type 
20×1hour lectures 
20 hours

SLT 
2×1hour problems/revision classes 
2 hours

SLT 
3×1hour tutorials

3 hours

SLT 
5×6hour selfstudy packages 
30 hours

GIS 
4×4hour problem sets 
16 hours

GIS 
Reading, private study and revision 
79 hours

GIS 
Assessment
Weight 
Form 
Size 
When 
ILOS assessed 
Feedback 
0% 
Guided selfstudy 
5×6hour packages 
Fortnightly 
18 
Discussion in tutorials

0% 
4 × Problems sets 
4 hours per set 
Fortnightly 
18 
Solutions discussed in problems classes. 
100% 
Final Examination 
2 hours 30 minutes 
January 
18 
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:

Eisberg R.M. and Resnick R. (1974), Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles, Wiley, ISBN 0471234648 (UL: 530.12 EIS)

McMurry S.M. (1994), Quantum Mechanics, Addison Wesley, ISBN 0201544393 (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 1214, Open University (UL: 530.12 OPE/X)

Open University SM355 Course Team (1986), Quantum Mechanics: Units 1516, Open University (UL: 530.12 OPE/X)

Park D. (1974), Introduction to the Quantum Theory (2^{nd} edition), McGrawHill (UL: 530.12 PAR)

Pauling L. and Wilson E.B. (1935), Introduction to Quantum Mechanics, McGrawHill (UL: 530.12 PAU)
ELE:
Further Information
Prior Knowledge Requirements
Prerequisite Modules 
Quantum Mechanics I (PHY2022) and Mathematics with Physical Applications (PHY2025) 
Corequisite Modules 
none 
Reassessment
Reassessment is not available except when required by referral or deferral.
Original form of assessment 
Form of reassessment 
ILOs reassessed 
Time scale for reassessment 
Whole module 
Written examination (100%) 
18 
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% 

Miscellaneous
IoP Accreditation Checklist 
 QM05 Wave function and its interpretation
 QM06 Standard solutions and quantum numbers to the level of the hydrogen atom
 QM07 Tunnelling
 QM08 First order time independent perturbation theory
 QM09 Quantum structure and spectra of simple atoms
 QM12 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 
01Oct10 
Revised 
29Sep14 