Question: Suppose V = cx8, where c is a positive constant, and we want all eigenvalues with Er < 10. (a) Show that Vr = x8r
(a) Show that Vr = x8r and that for Er = 10 the boundaries of the classically allowed region are at xr = ± 1.33.
(b) Set up a spreadsheet and verify that if we take xr, 0 = - 3, xr,max = 3, and sr = 0.05, ψ undergoes spurious oscillations for |xr| > 2.65.
(c) Verify that 1 - Grs2r /12 ≈ 0 for |xr| = 2.65, so 1 - Grs2r /12 is negative for |xr| 7 2.65.
(d) Use your spreadsheet to verify that the spurious oscillations are eliminated if we take either xr, 0 = -2.5, xr,max = 2.5, and sr = 0.05; or xr, 0 = -3, xr, max = 3, and sr = 0.02.
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a V is the same as in Prob 433 except that c replaces a From the Prob 433 solution ... View full answer
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