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Chapter Summary:

1. Visualization of Wave Functions

Although nobody can tell how a qantum-mechanical particle looks like, we can nevertheless visualize the complex-valued function (wavefunction) that describes the state of the particle. In this book complex-valued functions are visualized with the help of colors. By looking at Color Plate 3 and browsing through the section "Visualization" on the accompanying CD-ROM, you will quickly develop the necessary feeling for the relation between phases and colors. You need to study this chapter only if you want to understand the ideas behind this method of visualization in more detail and if you want to increase your familiarity with complex-valued functions. Here we derive the mathematical formulas describing the color map which associates a unique color to every complex number. This color map is defined with the help of the HLS color system (hue-lightness-saturation): The phase of a complex number is given by the hue and the absolute value is described by the lightness of the color (the saturation is always maximal). On the CD-ROM you will find the Mathematica packages ArgColorPlot.m and ComplexPlot.m which implement this color map on a computer. These packages have been used to create most of the graphics in this book and on the CD. In this chapter you will also find a comparison of various other methods for visualizing complex-valued functions in one and more dimensions. Finally, we describe some ideas for a graphical representation of spinor wave functions which will be used in Book Two.