(a) Use the Numerov method to find all the bound-state eigenvalues for a particle in a rectangular well (Section 2.4) of length l with V0 = 20h2/ml2. Note that V is different in different regions and ψ ≠ 0 at the walls.
(b) Repeat (a) for V0 = 50h2/ml2.
(c) Check your results using the automatic solver in your spreadsheet program or Mathcad to find the roots of Eq. (2.35). (Before doing this, find approximate values from a spreadsheet graph.)
Use either a program similar to that in Table 4.1, a spreadsheet, or a computer-algebra system such as Mathcad. If negative eigenvalues are being sought using Excel 2010, you must uncheck the Make Unconstrained Variables Non-Negative box in the Solver Parameters box.