Spherical Harmonics
This program is designed to visualize the spherical harmonics Ylm and cuts through them, which can be measured with the quantum analogs experiment. The three-dimensional plots for different quantum numbers l and m can be rotated and displayed light-shaded. A cut through the 3-D plot in the x-z-plane (azimuthal angle phi = 0) is displayed in blue when chosen. A cut at polar angle theta=45° is displayed in green when chosen. These cuts correspond to the measurements that can be performed in the "atom" with spherical symmetry (the blue one) and the "atom" with broken symmetry (the green one), respectively. The typical two-fold or four-fold symmetry for m=1 and m=2, respectively, is only visible when the real-part or the imaginary part is plotted instead of the absolute value. The program is for free. It has been tested carefully and should work with all current windows versions. However, we can not give any warranty that it will work with your individual computer. With downloading the program you agree that any liability is excluded.
The program is a single exe-file. After starting, three windows are opening. In the main window (top left) the quantum numbers can be chosen (angular momentum quantum number l and the magnetic quantum number m). In the right window a three-dimensional plot is shown. The object can be rotated and zoomed using the slider bars (left, bottom and right side of that window). If "light shaded" has been chosen in the main window, then there are two more sliders at the top that allow to adjust the position of the light source. In the lower left window a polar plot of Ylm(theta) is shown (displayed in blue). It corresponds to the measurement that can be done with the quantum analogs experiment at the spherical symmetric "atom" (amplitude as function of theta). When pressing the button "Show Azimuthal Plot" in the main window, another window opens that shows the Ylm as function of the azimuthal angle phi for a fixed polar angle theta=45° (displayed in green). This corresponds to the measurement that can be done with the quantum analogs experiment at the "atom" with broken symmetry (amplitude as function of phi). Both angular dependencies can be visualized in the three-dimensional plot by choosing "Cut polar angle" or "Cut azimuth". All graphs can be saved as jpeg or bmp images or can be printed directly using the menu.