PHY2022 
Quantum Mechanics I 
202324 

Dr C.L. Davies 


Delivery Weeks: 
T1:0111 

Level: 
5 (NQF) 

Credits: 
15 NICATS / 7.5 ECTS 

Enrolment: 
170 students (approx) 

Description
This module introduces the mathematical expression of the basic principles of quantum mechanics and methods for
finding solutions of problems that permit straightforward mathematical analysis.
These solutions demonstrate many of the general features of
the subject and will be applied in subsequent modules in the Physics programme.
Module Aims
Quantum Mechanics is one of the fundamental buildingblocks of Physics. It affects profoundly the
way we think about the universe and is the basis for much of condensedmatter, nuclear and
statistical physics. It also has a strong influence on technological developments, for instance in
optical and electronic devices. This module aims to give students a firm grounding in the subject and
to prepare them for future modules such as PHY3052
Nuclear and HighEnergy Particle Physics.
Intended Learning Outcomes (ILOs)
A student who has passed this module should be able to:

Module Specific Skills and Knowledge:
 describe the definition and interpretation of the wavefunction and of operators in quantum
mechanics;
 discuss the origin of energy quantisation and quantum tunnelling effects;
 describe the general properties of the stationary states of quantum particles confined to
simple symmetric potentials;
 perform calculations on wavefunctions, and solve the Schrödinger
equation for a range of problems;
 use timeindependent perturbation theory to solve problems and interpret results;
 explain the origin of the uncoupled set of quantum numbers for the hydrogen
atom and the form of the associated eigenfunctions;

Discipline Specific Skills and Knowledge:
 use the principles of quantum mechanics to solve problems;
 explain quantum mechanics to a layperson in an informed manner;

Personal and Key Transferable / Employment Skills and Knowledge:
 construct arguments that explain observations;
 solve problems by using mathematics;
 use a range of resources to develop an understanding of topics through independent study.
 meet deadlines for completion of work for problems classes and develop appropriate
timemanagement strategies.
Syllabus Plan

Introduction
Brief historical survey; recap of PHY1022;
what is required of the theory; the wave equation; timedependent Schrödinger equation

Wave Functions and their Interpretation
The Born probability interpretation; normalization of the wave function; first postulate;
wave function of a free particle; wave function of a confined particle;
Gaussian wave packets (Selfstudy pack): the uncertainty principle; time evolution of wave packets

Dynamical Variables
Observables as operators; the second postulate; the third postulate;
physical significance of eigenfunctions;
Schrödinger equation revisited

Stationary States and the TimeIndependent Schrödinger Equation
Timeindependent probability distributions; the timeindependent Schrödinger equation;
stationary states: eigenfunctions of the Hamiltonian;
example: region of constant potential; method of solution ; boundary conditions

Particle in a Box  the Infinite Square Well
Internal solution; boundary conditions; energy quantization; normalized wave functions

The Finite Square Potential Well (Selfstudy pack)
Interior and exterior solutions; boundary conditions; symmetric solutions  energies and wave functions;
antisymmetric solutions  energies and wave functions

Flow of Particles
Probability flux; continuity equation; persistence of normalization; derivation of probability flux

Barrier Problems
Boundary conditions at a potential discontinuity; a potential step;
tunnelling: reflection and transmission by a barrier;
practical examples of tunnelling

Quantum Measurement and the Structure of Quantum Mechanics
Properties of Hermitian operators; the superposition principle: fourth postulate;
measurements of a general quantum state; commutation relations and simultaneous observables;
the uncertainty principle; commutation with the Hamiltonian;
summary: the postulates of quantum mechanics

The Quantum Harmonic Oscillator
Hamiltonian in operator form; ladder operators; eigenvalues and eigenfunctions

The 3D TimeIndependent Schrödinger Equation
Momentum eigenfunctions in 3D;
Schrödinger equation in 3D Cartesian coordinates (Selfstudy pack);
example: particle in a 3D box;
Schrödinger equation in spherical polar coordinates

Angular Momentum
Cartesian representation of angular momentum operators; commutation relations;
polar representation of angular momentum operators; eigenfunctions and eigenvalues;
example: Rotational energy levels of a diatomic molecule

The Hydrogen Atom
Solutions of the angular equation; solutions of the radial equation;
energy eigenvalues  the hydrogen spectrum; electron density distributions

FirstOrder TimeIndependent Perturbation Theory
Perturbation theory for nondegenerate levels; perturbation theory for degenerate levels
Learning and Teaching
Learning Activities and Teaching Methods
Description 
Study time 
KIS type 
22×1hour lectures 
22 hours

SLT 
5×6hour selfstudy packages 
30 hours

GIS 
8×2hour problems sets 
16 hours

GIS 
Problems class support 
8 hours

SLT 
Tutorial support 
3 hours

SLT 
Reading, private study and revision 
71 hours

GIS 
Assessment
Weight 
Form 
Size 
When 
ILOS assessed 
Feedback 
0% 
Exercises set by tutor 
3×1hour sets (typical) 
Scheduled by tutor 
112 
Discussion in tutorials

0% 
Guided selfstudy 
5×6hour packages 
Fortnightly 
112 
Discussion in tutorials

10% 
8 × Problems sets 
2 hours per set 
Weekly 
112 
Marked in problems class, then discussed in tutorials

15% 
Midterm test 
30 minutes 
Weeks T1:06 
111 
Marked, then discussed in tutorials

75% 
Examination 
120 minutes 
January 
111 
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:

Rae A.I.M. (2007), Quantum Mechanics (5^{th} edition), Chapman and Hal, ISBN 1584889705
Supplementary texts:
ELE:
Further Information
Prior Knowledge Requirements
Prerequisite Modules 
Mathematics for Physicists (PHY1026) 
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%) 
111 
August/September assessment period 
Notes: See Physics Assessment Conventions.
KIS Data Summary
Learning activities and teaching methods 
SLT  scheduled learning & teaching activities 
33 hrs 
GIS  guided independent study 
117 hrs 
PLS  placement/study abroad 
0 hrs 
Total 
150 hrs 


Summative assessment 
Coursework 
10% 
Written exams 
90% 
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

Availability 
unrestricted 
Distance learning 
NO 
Keywords 
Physics; Energy; Eigenvalues; Eigenstates; Hydrogen Atom; Observables; Particles; Perturbation theory; Quantum mechanics; Schrödinger equation; Time; Waves. 
Created 
01Oct10 
Revised 
01Oct11 