Developed by Jamie Lombardi (jlombard@alleg.edu), Physics Department, Allegheny College, Meadville PA, 16335.
Category: Physics (Quantum Mechanics)
Hydrogen displays plots of wave-functions and probability distributions for an electron of a hydrogen atom.
The user can set the principle quantum number n, the angular momentum l and the magnetic moment m by using sliders or text fields.
Through separation of variables, the total wave function of a hydrogen atom (which depends on n, l and m) can be expressed as a radial function R(r) multiplied by a spherical harmonic Y. The user is aided in the visualization of these wavefunctions by five separate views. A "Plot All" button plots all five, or, to look at one of the graphs, the user can simply the "Plot" button immediately below the appropriate view.
The view in the upper left-hand corner shows the radial wave function R(r), while the view in the upper right view shows the radial probability distribution of the electron. Both of these functions can be plotted by pressing the "Plot Both Radial Functions" button located between the two top views. In both plots, r is given in units of Bohr radii. A Bohr radius is about 0.53 angstroms.
The remaining three graphs are polar plots. The lower left view shows the angular wave function, while the lower right view gives a polar plot of the angular probability distribution. Both of these angular functions can be plotted by pressing the "Plot Both Angular Functions" button located immediately below the "Quantum Numbers" box.
Finally, the middle plot shows the planar distribution for the electron, with white areas representing regions in which the electron is likely to be found. The program automatically picks a good resolution, but this can be adjusted by the slider or text field immediately below the view.
Questions concerning the main points of this program can be displayed by choosing the "Questions" menu item. The user can save answers in a notebook which can be opened under the "Answers" submenu.
Hydrogen is used in Quantum Mechanics and Quantum Chemistry at Allegheny College to help students visualize wave-functions of atoms such as hydrogen.
This application was developed under NeXTstep release 2.0.
NOTE: Since graphs of "Hydrogen" are generated by Mathematica, Mathematica.app should be in the NextApps, LocalApps, or ~/Apps directory.
