Now we must modify the steps for sketching wave function and include both oscillating and decreasing shapes. The shape of a wave function depends upon the Total Energy and Potential Energy. If the potential energy is less than the total energy, the wave function is oscillating. If the potential energy is greater than the total energy, we get a decreasing wave function. Step 2 must be modified to include both possibilities. Below is a list of the steps that will work for all cases.
Creating Wave Functions
1. Consider the physical situation, draw the energy diagram
and determine the boundaries.
2. Use the total and potential energies to determine if the wave
function is oscillating or decreasing, then follow A or B below.
A. Oscillating: Determine the wavelength for the oscillations.
B. Decreasing: Determine the decrease length. Then, sketch the
wave function.
3. Adjust the phases and amplitudes until the wave function is
smooth across all boundaries.
4. Interpret the probability density and discuss the probability
of finding the object at various locations.