0.2 Numerical Solution to the Finite Well infinite infinite :w=2,5,10 nm : 0.3eV, leV, 10ev b Figure 1: Create a numerical Hamiltonian for this potential profile 1. Based on the Matlab code available on the website, create your own MATLAB code (Python also accepted) to simulate the potential profile shown above. In your calculations please use an effective mass of m* = 0.067m,, where my is the rest mass of the electron. 2. In your code extend b until the eigenstates inside the well (bound states) do not change significantly (you determine the threshold); i.e. only the states whose energy is less than the top of the well. Please note, that b is the dimension on both sides of the well not just the right; i.e., both sides must be extended. 3. Plot the energy vs the quantum number n, where n is the index of each eigenvalue. 4. Plot the wavefunctions in the well superimposed on the potential profile at a height E. 5. Compare the results for the different parameters, as well as against the results of the infinite potential well. Note: In all cases you only have to consider the states whose energy falls within the well (bound states)