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Unformatted text preview: . 1 The most convenient basis functions φ n ( x ) to use are the ones that are the eigenstates of the particle in a box problem, φ n ( x ) = r 2 L sin ± nπx L ² In this basis, we have ± n = ~ 2 n 2 π 2 2 mL 2 2. Solve the problem above using a computer program that diagonalizes the matrix H . Give the lowest ﬁve eigenvalues and plot the lowest ﬁve wave functions ψ ( x ). Experiment for diﬀerent values of nmax . At what point do the lowest ﬁve eigenvalues not depend strongly on nmax ? Use (as usual) ~ = m = 1. 3. Use a numerical implementation of perturbation theory to ﬁrst and second order to estimate the eigenvalues. Compare to the exact results above. Does this tell you whether the perturbation can be regarded as small? Note that the elements of your matrix H mn already contains the terms that are needed to do the perturbation theory estimate. 2...
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This note was uploaded on 08/08/2011 for the course PHZ 5156 taught by Professor Johnson,m during the Fall '08 term at University of Central Florida.
- Fall '08