(a) For the harmonic-oscillator Numerov example, we went from - 5 to 5 in steps of 0.1 and found 0.4999996 as the lowest eigenvalue. For this choice of xr, 0 and sr, find all eigenvalues with Er < 6; then find the eigenvalue that lies between 11 and 12 and explain why the result is not accurate. Then change xr,0 or sr or both to get an accurate value for this eigenvalue.
(b) Find the harmonic-oscillator eigenvalues with Er < 6 if we go from -5 to 5 in steps of 0.5.
(c) Find the harmonic-oscillator eigenvalues with Er < 6 if we go from -3 to 3 in steps of 0.1.
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.