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Appendix

BlochApp allows the user to examine the three dimensional structure of the path of the Bloch vector, but BlochApp does not allow the user to perform a real time rotation of this path because it is unneeded when examining the fundamental physics; however, Mathematica can easily perform this task.

Open Mathematica and load the Graphics3D and Animation packages with the commands, . Use the SetDirectory command to indicate where the data file has been placed on your computer. The data can now be loaded into memory via a command like, which will load the information from the data.3d file into the list variable, BlochData. The three occurrences of the word, "Number," signify that a three dimensional point must be loaded.

Once BlochData has been defined, the data is plotted. The ScatterPlot3D command in the Graphics3D package will plot it in three space. The data has been saved in the order that it was created, i.e., the first point in the data list was the initial position of the Bloch vector, etc. Connecting these data points will recreate the same image that was observed in BlochApp. The data points can be connected by setting the PlotJoined option to True. The full plotting command should look like:

Notice that the output graphic has been saved in BlochPic.

The SpinShow command in the Animation package will generate the data for a real time rotation of BlochPic. The command is quite simple, . The Frames option sets the number of frames in the output Mathematica movie. Setting this number smaller will speed up the render time, but the result will not look as fluid.

A complete Mathematica file, which is called BlochRot.ma, has been included to further illustrate this technique. A sample export file, data.3d, has also been included.


next up previous contents index
Next: References Up: An Examination of Atom--Field Previous: Epilogue



Andy Antonelli
Wed May 17 14:34:24 EDT 1995