2/PH/SB QUANTUM PHYSICS
Aims
The unit aims are to provide an introduction to quantum physics and to encourage the development of
independent learning skills.
Summary
The unit syllabus is defined by the coverage of 10 FLAP modules. These comprise 3 modules on atomic
structure (with an additional background module as required) and 7 modules on quantum physics.
The atomic physics ranges from simple ideas of atomic constituents, through the Bohr model for
hydrogen to the structure of multi-electron atoms and the periodic table of elements. In quantum
physics the range is from the particle model for light and the wave model for matter, through the
complex wavefunction and the Schrödinger equation to its application in barrier reflection, tunnelling,
the harmonic oscillator and the hydrogen atom. The pedagogic style is supported self-study, with ten
lectures, eight short videos and ten workshops.
Learning outcomes
The learning outcomes for each FLAP module are specified in detail in the module’s Achievements
subsection and so the learning outcomes for this unit are given by the sum total of all the Achievements
subsections for the modules included in the unit. To this list should be added the independent
learning skills of reading for information and the organizational skills of self-directed learning and
working flexibly, but to deadlines. The overall learning outcomes of the modules may be summarized as
follows.
After the unit, a student should be able to:
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Define all the glossary terms specified;
Describe the structure of an atom, an ion and an isotope in terms of its constituents, its
atomic mass, mass number and atomic number;
Describe the processes of emission and absorption of electromagnetic radiation in atoms
and how these may be studied experimentally;
Explain why atoms have characteristic spectra and how this is useful;
Describe black body radiation and how this depends on temperature;
Use Balmer’s formula for the visible lines of atomic hydrogen;
Describe the Bohr model for atomic hydrogen, identify its postulates and derive expressions
for the radii of Bohr orbits, the energy levels, the ionization energy and the wavelengths and
frequencies of spectral lines;
Use the Bohr model to derive Balmer’s formula;
Sketch the energy level diagram for atomic hydrogen in terms of the principle quantum
number, showing possible transitions;
Explain how the technique of photoelectron spectroscopy can be used to obtain
information about the electronic structure of atoms;
Explain how the quantum state of an atom can be characterised by four quantum numbers,
outlining their physical meaning, and how this leads to electron shells and subshells;
Use the empirical rules for shell and subshell closures, together with the s-p-d-f notation
and Hund’s rule to write down the electronic structure of atoms in their ground states;
Interpret the experiments of Zeeman and of Stern and Gerlach;
Explain the origins of continuous and characteristic X-ray spectra;
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Outline the structure of the periodic table and explain its relationship to the electronic
configuration of atoms;
Describe the main features and consequences of the electronic configuration of the main
group elements, the transition elements, the lanthanides and the actinides;
Use the concept of valency to predict the structure of simple chemical compounds;
Describe the characteristics of ionic, molecular covalent, extended covalent and metallic
bonding, and their consequences for the material;
Draw Lewis structures for simple chemical compounds;
Describe the essential experimental features and the need for a quantum interpretation of
the photoelectric effect and the Compton effect;
Calculate photon energies and photon momenta and relate these to the wavelength and
frequency of the associated electromagnetic radiation;
Describe and illustrate the wave/particle duality behaviour of light;
Recall and use the de Broglie relationship for the behaviour of matter;
Describe and use the probabilistic interpretation of a de-Broglie wave;
Recall and use the Heisenberg uncertainty principle for position and momentum and for
energy and time;
Identify situations where quantum physics supersedes classical physics and describe the
Copenhagen interpretation of quantum theory;
State and use the probabilistic interpretation of the wavefunction;
Represent a free particle as a single complex travelling wave or as a wave packet and relate
this to Heisenberg’s uncertainty principle;
Recall and use the expressions for total energy, momentum and kinetic energy for a free
particle in a single travelling wave representation;
Recall the spatial wavefunctions for a confined particle in a one-dimensional box and show
that these lead to definite energy states;
Define and use the differential operators for momentum and kinetic energy for a particle
moving in one dimension;
Determine whether a function is an eigenvalue of an operator and use an eigenvalue
equation to determine eigenvalues and observables;
Recall the time-independent Schrödinger equation for a free particle moving in one
dimension, with and without a potential energy function, and use this equation, together
with appropriate boundary conditions, to obtain the eigenfunctions and energy eigenvalues
for a particle in a one-dimensional box;
Recall the Born probability interpretation of the wavefunction and relate this to the idea of
a stationary state and to normalization;
Recall the time-dependent Schrödinger equation for a particle moving in one dimension;
Use the Schrödinger equation to describe the behaviour of a particle incident on a
potential step or a potential barrier, calculate the reflection and transmission coefficients
and contrast this with classical behaviour;
Write down the Schrödinger equation for the harmonic oscillator, verify and sketch the
first few eigenfunctions and verify the eigenvalues;
Recall and use the general formula for the energy eigenvalues of the harmonic oscillator
and calculate the probability density functions;
Compare and contrast the classical and quantum results for the harmonic oscillator and
indicate when the quantum model is required;
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Write down the time-independent Schrödinger equation for the electron in the hydrogen
atom;
Identify and use the quantum numbers n, l, and ml for the electron in the hydrogen atom
and relate these to physical quantities, giving the allowed values for the quantum numbers
and the physical quantities;
Recall the expression for the energy levels of atomic hydrogen according to the Schrödinger
model and calculate frequencies and wavelengths of transitions between these levels;
For simple cases, sketch the radial wavefunctions and the radial probability densities for the
stationary states of atomic hydrogen, giving their spectroscopic classification;
Compare and contrast the predictions of the Bohr model and the Schrödinger model for
atomic hydrogen and relate this to the correspondence principle.
Prerequisites
The unit assumes mathematical skills at the level of 1/PH/H and a basic physics background
appropriate to 1/PH/A1 and 1/PH/L1. The prerequisites for each FLAP module within the unit are
specified in detail in each module’s Ready to study? subsection.
The physics prerequisites of the unit as a whole may be summarized by stating that a student should be
familiar with the concepts of:
 absolute temperature, acceleration, angular frequency, angular momentum, Boltzmann’s constant,
centripetal force, circular motion, conservative force, Coulomb’s law, diffraction, diffraction
grating, diffraction grating relation, dispersion, elastic collision, electric charge, electric current,
electric field, electric potential energy, electromagnetic radiation, electromagnetic spectrum,
electron volt, electrostatic force, energy conservation, force, frequency, interference, kinetic energy,
magnetic field, mass, momentum, momentum conservation, Newton’s laws of motion, nucleus,
orbit, orders of diffraction, potential difference, potential energy, principle of superposition,
pressure, radioactivity, simple harmonic motion, speed, standing wave, transverse wave, travelling
wave, vector, velocity, voltage, wave intensity, wavelength, wavenumber, wave speed and X-rays.
The mathematics prerequisites of the unit as a whole may be summarized by stating that a student
should be familiar with:
 algebraic functions, including trigonometric, exponential and logarithmic functions;
 vectors and vector notation;
 complex numbers as represented in Cartesian, polar and exponential forms and complex algebra,
including Euler’s formula;
 differential and integral calculus as applied to the functions listed above and the relationship to
graphical slopes and areas;
 homogeneous second-order differential equations with constant coefficients (e.g. SHM equation)
and their general solutions.
Teaching, Learning, and Assessment Strategy
The diversity in student backgrounds suggests a flexible learning strategy based on the supported selfstudy of FLAP modules. There is a particular problem in the general lack of core atomic concepts in
some A-level physics syllabuses, these being better covered in A level chemistry. This problem can be
addressed by using FLAP module P8.1, Introducing atoms, as background material for some students.
The style of FLAP modules encourages more independent, active learning and this is known to produce
more effective learning. In 2/PH/SB the student studies a selection of FLAP modules on a clearly
defined schedule and with regular (2-weekly) testing of progress to provide feedback for students and
teacher. These tests are ‘open book’. Weekly workshop sessions provide individual help as required
and a strong level of interaction between students and between staff and students. Ten lectures are
included and students suggest topics for these, after reading the modules. This produces a set of well-
targeted lectures, involves the students in the course design and marks the lectures out as supportive
rather than sufficient.
Student progress is checked regularly through the tests. By allowing students to have access to the full
range of modules for the term they are able to allocate their time appropriately, giving more time to
unfamiliar material and less time to familiar topics, always with an eye to the dates on which particular
modules are to be tested. The assessment is split into five 1 hour continuous assessment tests (50%),
covering two modules each, and one final 1-hour closed book examination (50%), covering the whole
unit, taken with Part II in April. The pass requirement is 40%, with a re-sit examination, if required, in
September, with no continuous assessment element.
Term(s):
Unit Code:
Department:
Pre-requisites:
Co-requisites:
Excluded units:
Required for:
Convener:
Lecturer:
Summer
Size of unit:
1
2/PH/SB
Modules:
PH302
Physics
1/PH/A1 & 1/PH/L1 (or near equivalents)
None
None
Some Part 2 and Part 3 Physics units
Dr M H Tinker
Dr M H Tinker
Teaching and learning methods:
FLAP (Flexible Learning Approach to Physics) based teaching method supplemented by Lectures,
workshops, directed reading and problem solving.
Contact hours:
Lectures
20
Workshops
10
Assessment
Weight
Continuous Assessment (Regular tests)
50%
Formal University Examination (2 hours, April)
50%
Requirement for pass:
Re-assessment:
An average of at least 40%
2 hours examination in September
15 March 2001