### Hydrogen Wave function Simulation

 n= l= m=

### Description:

This simulation calculates the wave functions for hydrogenic (hydrogen like) atoms for quantum numbers n = 1 to n = 50. The upper left window shows the angular wave function, the upper right window shows the radial wave function and the lower left window shows a plot of the  probabilitydensity (wave function squared) in the x - z plane.

Much like the case of an electron trapped in a one dimensional well the electrons of hydrogen like atoms are trapped around the atom in the coulomb potential. The wave functions representing the electron therefore have to 'fit' in the coulomb potential with the right boundary conditions.

You can enter various numbers of the three principle quantum numbers n, l and m in the window on the lower right.

### Question 1:

Look at the n = 1, l =m = 0 case. Hold the mouse down on the radial wave function graph (upper right window) and find the value of the wave function at distances 1, 2, 3, 4 (in units of 4/ao where ao is the Bohr radius). Now move the mouse to the probability density window (lower left) and note the intensity of the picture at the same distances from the center. How does the probability density relate to the curve shown in the radial wave function window?

### Question 2:

Look at the n = 2, l =m = 0 case. What does the back band in the probability density window (lower left) represent? How does it relate to the radial wave function (upper right window)? (Hint: Hold the mouse down on the probability density in the center of the dark band, record the radius (in units of Bohr radii) and then find the location where the radial wave function is zero by the same method.)

### Question 3:

Look at the cases n = 2, l = 1, m = 0 and n = 2, l = 1, m = 1. How does the angular wave function (upper left window) relate to the probability density? At approximately what distance does the probability for finding the electron diminish to zero?

### Question 4:

Look at the cases n = 3, m = 0 for the l values 0, 1, 2. Drag the mouse around in the probability density widow to determine approximately where the probability for finding the electron goes to zero. How does the size of the atom for this energy level with different l values compare? How does the size of the atom with electrons in the n = 3 energy level compare with the size of the atom with electrons in the n = 2 and n = 1 levels?

### Question 5:

Explain the probability density pattern for the case n = 4, l = 2, m =1 in terms of the radial and angular wave functions.