Quantum Mechanics
12 lectures in MT and 15 lectures in HT
Prof J.J. Binney
This is the first of two courses
that cover paper A3 in Part A of the three- and four-year physics
courses. The syllabus is given in the Course Handbook.
Goals of the
course
After working through this course
you should understand how probabilities are obtained from quantum
amplitudes, why they give rise to quantum interference, the concept
of a complete set of amplitudes and how this defines a "quantum state".
You should understand why each observable is associated with a
Hermitian operator, and how the latter is used to calculate the
expectation value of the observable. You should understand the
connection between the momentum and angular-momentum operators and
translations and rotations of states, and the connection between this
aspect of operators and commutation relations. You should have
understood the connection between symmetries and conservation laws.
You should be familiar with the
energy, position and momentum representations. You will have used
the position representation to understand the position/momentum
uncertainty principle and used the energy representation to study the
dynamics of both harmonic and anharmonic oscillators. You will have
studied the energy levels of particles interacting with various
one-dimensional potential wells and used the results to understand the
workings of an ammonia maser.
You will have determined the
eigenvalues of the total and orbital angular-momentum operators and
understood the difference betwen the transformations that they
generate. You will have understood how the kinetic energy of a particle
can be broken down into radial and tangential contributions. You will
have constructed both the Pauli
matrices to handle problems involving spin-half particles, and the
corresponding matrices for spin-one particles. You should understand
the connection between a particle's spin and orientation. You should be
familiar with the gross-structure spectrum and stationary states of
hydrogen.
There will not be time to describe
the history of quantum mechanics. This is a fascinating story but
rarely well told - most books try to combine the history with a potted
account of the science. Worthwhile are "Inward Bound" by A. Pais (OUP)
and "Fundamentals of Modern Physics" by J.J. Eisberg (Wiley). Werner
Heisenberg's collection of essays "Across the Frontiers" (originally "Schritte
ueber Grenzen") gives a gripping first-hand perspective on the later
half of the development of quantum mechanics (and of life in Germany
during the first half of the 20th c).
Synopsis
The presentation will closely follow
that in
The Physics of Quantum Mechanics,
James Binney and David Skinner, Oxford University Press 2014. A slightly obsolete version is downloadable gratis at
B&S.
The division into lectures is only
approximate
1 Amplitudes, quantum states, the
energy representation
2 Dirac notation & the energy representation
3 Operators and observables
4 The TDSE, the position
representation
5 Particle dynamics
6 Wave functions of well-defined
momentum and the uncertainty principle
7 Two slits revisited, extensions
to three dimensions, virial theorem
8 Harmonic oscillator: the
stationary states
9 Dynamics of oscillators
10 Transformations and
observables:
transformations of kets
11 Transformations and
observables: transformations of operators
12 Symmetries & conservation
laws, geometry and commutators
13 The square well
14 A pair of square wells, ammonia
maser
15 Tunnelling and radioactive decay
16 Composite systems &
entanglement
17 Einstein-Podolski-Rosen R
experiment & Bell inequalities
18 Angular momentum; eigen values
of J_z and J^2
19 Spectra of diatomic molecules
20 Orbital angular momentum,
generation of circular translations
21 Eigenfunctions of L_z and L^2; radial/tangential decomposition
of KE
22 Spin
23 Stern-Gerlach experiment and spin 1
24 Classical spin & the
addition of angular momenta
25 Gross structure of hydrogen
26 The emissinn spectrum of
hydrogen
27 Eigenfunctions of hydrogen
Videos of the lectures
Problem sets
MT1 MT2
Christmas Vacation
HT1 HT2 HT3 Easter Vacation
all
Books
The Physics of Quantum Mechanics,
James Binney and David Skinner, Oxford University Press 2014 about £25
The course is based on the first 8 chapters of this book, and the
remaining chapters cover the rest of the second-year material and
some more.
A slightly obsolete version can
be downloaded gratis from here
A Modern Approach to Quantum Mechanics,
J.S. Townsend.
McGraw Hill
published a paperback edition but now it
seems to be available only in hardback at £54 from University
Science Books. This was once my favourite undergraduate text for QM because
it has a clear logical structure and doesn't waste time on history.
Modern Quantum Mechanics,
J.J. Sakurai. Addison Wesley gives quite a
similar perspective to that of the course. Only available in hardback
at about £50
Quantum Physics, Stephen
Gasiorowicz, Wiley £25. A good traditional text at the right
level. However, I don't like the traditional approach.
The Feynman Lectures vol 3, R.P.
Feynman, R.B. Leighton & M. Sands, Addison Wesley £32.
Feynman was one of the great physicists of the last century and had
unique insight into QM that comes across in this book. Well worth
studying to see how Feynman approaches a problem. The trouble is, his
approach generally isn't algorithmic but depends on his remarkable
physical insight, so it isn't easy to emulate.
The Principles of Quantum Mechanics,
P.A.M.
Dirac,
Oxford
University
Press £31.35. Dirac contributed
as much to QM as anyone and this book is based on the lectures he gave
in Cambridge for the Mathematical Tripos. His arguments can be so
elegant you miss them, so close reading is essential. But the power and
clarity with which he lays out the ideas and obtains results is
awesome. Not for the mathematically challenged, but if you like
mathematics, do give it a try.