IB Quantum Mechanics

Lecturer: Adrian Kent
Michaelmas Term 2018, 16 lectures, Tuesday, Thursday at 11am in Mill Lane lecture room 3

Printed lecture notes and slides

This page contains updated versions of the printed lecture notes and other course materials.
The latest version of the lecture notes is dated 11.11.18. The online notes are now in one file
and contain all the figures from the printed notes distributed in the first lecture.

Lecture note updates 15.10.18: included a short discussion of the Born rule for
finite interval position measurements, and corrections to eqns. (7.59) and (7.60).

Lecture note updates 19.10.18: replaced partial derivatives wrt x by total
derivatives in the time-independent Schrodinger equation (4.6) and later
equations in section 4. Replaced k by k' in discussion of transmitted
waves in section 5.1.

Lecture note updates 29.10.18: comment added on the positive definiteness
of the inner product on wavefunctions.

Lecture note updates 11.11.18 Important comments added on the general
definition of expectation value (p45). Comments added on the commutator
(p46). Discussion of periodic table corrected (p66).

Lecture note updates 14.11.18 Comment added on the definition
of the inner product in 3D QM, Eqn (7.13) clarified and extended. (p54)

Lecture note updates 16.11.18 Comments added at the end of section 7.2
on the extension of theorems 6.1-6.3 to 3D. Notation in section 7.2
corrected to refer to 3d vectors as underlined x. Minus sign
corrected in equation (7.73). [Also leading spaces removed in
some subsection headings, one comment in text transferred to footnote.]

Lecture note updates 05.12.18 Various small typos corrected.

Slides of all course lectures are now available.

Common problems in learning quantum mechanics and 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

Videos: double slit experiment

A video of a double slit experiment for electrons can be found at
https://www.youtube.com/watch?v=1LVkQfCptEs

A video of a double slit experiment for large molecules can be found at
https://www.youtube.com/watch?v=wDx8tu-iX8U

A simulation of a wavepacket going through a double slit can be found at
https://www.youtube.com/watch?v=jHyO0A7C86E

Videos: 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.)

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

A short overview of scanning tunnelling microscopy and spectroscopy is at
https://en.wikipedia.org/wiki/Scanning_tunneling_microscope
(Video link on right hand side of wiki page.)

Videos: Ehrenfest's theorem

A nice illustration of Ehrenfest's theorem is given by calculating the
expectation value of the position of a wave packet in a harmonic oscillator potential,
which follows the same trajectory as a classical point particle
in the same potential. This is true for general wave packets,
and easy to follow visually for a Gaussian wave packet, because the expectation
value of the position corresponds to
the peak of the Gaussian. A short video simulation is at
https://www.youtube.com/watch?v=1fMi1nriS8Q

Videos: other

An interpretative dance inspired by quantum tunnelling (don't take the
accompanying explanations of tunnelling too seriously) can be found here:
https://vimeo.com/129387271

Demonstrations

The experimental demonstrations in the lectures can easily be reproduced
using a laser pointer (ideally not heavily polarised), a diffraction
grating, and a set of polarizer slides. Gratings and slides
can be obtained cheaply online, for example here:

https://www.amazon.co.uk/gp/product/B0074R9PXA/ref=oh_aui_search_detailp...
https://www.amazon.co.uk/gp/product/B01GQ0KZNY/ref=oh_aui_search_detailp...

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