Using the Wave Packet Explorer program, try an amplitude-momentum distribution similar to the one in Figure 5.
Figure 5: An amplitude-momentum distribution that gives a wave function similar to the one in Figure 3.
To come even closer you can add a very large number of momenta. Hold down the shift key and the left mouse button and drag the cursor across the amplitude-momentum graph. This process adds together all of the wave functions with momenta and amplitudes in the shaded region.
You can look at any one wave function in all of the collection by moving the mouse over the line in the momentum graph. Both the momentum line and the corresponding wave function in the bottom graph will turn green.
Make a sketch of the resulting position wave function.
What is the probability interpretation of the wave function?
Does this wave function have a large or small range of momenta associated with it?
Now try a wave function which has a very narrow range of momenta. Create it by dragging over a small range.
How is the probability interpretation different from the previous wave function?
Now, using Wave Function Sketcher, try to create · a wave function that represents a high probability of the electron being in a very small region of space, and · a wave function that represents an electron that has equal probabilities of being in many different regions.
How do these wave functions (and the momenta represented by them) differ?