IB Quantum Mechanics
Lecturer: Adrian Kent
Notes and supplementary material for course taught in 2019-20.
Full lecture notes (minor corrections 31.12.19 and 16.05.20)
Lecture notes part 1 (completed)
Lecture notes part 2 (completed)
Lecture notes part 3 (completed)
Lecture notes part 4 (completed)
Slides on fission, fusion and the tunnelling electron microscope (non-examinable)
Slides on existence and uniqueness of hermitian conjugate (non-examinable)
Slides on why position and momentum measurements are approximate (non-examinable)
Slide on measurement of a degenerate eigenvalue
Slides on photon polarization measurements (non-examinable)
Slide on uncertainty and statistical variance
Slides for lecture 12 (uncertainty, Ehrenfest, harmonic oscillator)
Slides for lecture 13 (QM in 3D; central potentials)
Slides for lecture 14 (Hydrogen atom spherically symmetric states; angular momentum)
Slides for lecture 15 (Full solution of Hydrogen atom)
Links to resources
Research suggests that students learning quantum mechanics for the
first time encounter similar problems and temporary confusions.
This seems to be true for students with a wide range of backgrounds
and aptitudes. The article below discusses some points where
confusion often arises: you may want to test yourself on the
questions. It also gives links to a range of simulation tools
designed to build and test intuitions about quantum mechanics.
https://physicstoday.scitation.org/doi/10.1063/1.2349732
Double slit experiment
Tonomura's double slit experiment is discussed here, with a link to the narrated video:
https://www.hitachi.com/rd/portal/highlight/quantum/doubleslit/index.html
Arndt's group's experiments on large molecule interferometry are described here:
A simulation of a wave packet in a double slit experiment is here:
https://www.youtube.com/watch?v=jHyO0A7C86E
Gaussian wave packets
A nice discussion of some of their properties, with simulations, is at:
https://www.cond-mat.de/teaching/QM/JSim/wpack.html
Scattering and tunnelling
Simulations of wavepacket scattering from various potentials can be found at
https://www.youtube.com/watch?v=mmLDtkpg3wQ
(near perfect reflection from a square potential with U>>E)
https://www.youtube.com/watch?v=TQIMQzw_-lQ
(scattering and transmission from a step potential: note that
the wavelength of the transmitted wave is longer, because
it loses some momentum in climbing the potential step.
This simulation gives a clear picture of wavepacket reflection and
transmission up to about 0.06; reflecting endpoint boundary
conditions confuse the picture after that.)
Scattering of a 2D wave packet from a potential:
https://www.youtube.com/watch?v=8qOXof9_34M
Simulations of reflection from and tunnelling through a square potential barrier
can be found at
https://www.youtube.com/watch?v=4-PO-RHQsFA
https://www.youtube.com/watch?v=_3wFXHwRP4s
Lecture notes part 4 (completed)Reflection from and tunnelling through square potential well and barrier:
https://www.youtube.com/watch?v=cV2fkDscwvY
A nice review of the significance of tunnelling in some chemical reactions:
https://science.sciencemag.org/content/299/5608/833
Ehrenfest's theorem
Illustration of a Gaussian wave packet in the harmonic oscillator potential: