Dr Christopher W P Palmer

University of Oxford
Department of Physics
and
Balliol College

Home 1st year Maths Teaching 2nd year E&M Teaching Old Data Analysis Lectures Old Normal Modes and Waves Lectures Old S8 Lectures Old Further QM Lectures Old Electromagnetism Lectures Mechanics of the Atom

Visualisations Over the Years I have created a number of visualisations of physical phenomena, and these are collected here Wavepacket Plotter. This allows the user to specify a quantum superposition state for the one-dimensional particle in a box, and then display the time-development of the resulting wavepacket. This is the oldest of the visualisations - its origins go back to the 1990s - and many features have been added to it. The user interface is hence quite busy! To use it, first select the parameters of the wavepacket: quantum numbers, coefficients (uniform or smoothly varying), and initial phase difference between consecutive quantum states. Then click Make Wavepacket. (Alternatively, accept the default wavepacket which is displayed on opening the page, which uses all states from quantum number 90 to 110 inclusive.) Now switch to the Plot Menu and choose from a range of options, either displaying the wavefunction at a fixed time, or the development over a range of times. NEW upgraded to version 2.1: Wigner representation now works.

Dispersive Wavepacket Plotter.
This has something in common with the QM Wavepacket Plotter above, but this is entirely classical. It shows the time development of a surface wave on water, with a choice of three different dispersion relations. Optionally it also displays the fixed envelope. The user interface is much simpler and is well explained on the page.

Dynamics of Plucked string
This shows the time development of a tensioned string plucked at a quarter of its length. Because the wave satisfies the wave equation, the solution can be written as a sum of forwards and backwards travelling waves, and these are also shown.

EM Potentials for Long Permanent Magnet.
EM Potentials for Short Permanent Magnet.
EM Potentials for Disc Permanent Magnet.
These display the EM potentials of a certain charge distribution. Plot 1 (same in all three versions) can be interpreted as the potential for a uniform disc of charge, either electric, or magnetic (for example the end face of a uniformly magnetized cylinder). In the magnetic case the gradient of the potential is H. The axis is horizontal, and the potential is shown on a colour scale, so that changes of colour indicate the equipotentials. The potential is calculated as the first twelve terms of an infinite series. Plot 2 shows the error in Plot 1 on the axis, where there is a simple analytic form for the porential. You can see that the error is largest at z=a, where the series changes from ascending to descending powers of z. Plot 3 superposes two charged discs of opposite charge with different length:radius aspect ratios. Again this can be interpreted either as a magnetic or electric example. The Magnetic Disc case, in the electric interpretation of this plot, is close to a parallel plate capacitor, but it is evident that the potential of each plate is not constant for this uniformly charged example. Plot 4 shows the B field in the magnetic case, again as a potential whose gradient is the field. Of course the B field cannot be represented by a potential everywhere, and the potential shown is discontinuous in the centre of the cylinder, where the colour changes from black (maximum negative potential) to white (maximum positive).

C W P Palmer, University of Oxford.

This page updated December 2023