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Topic: Science
Number of pages / Number of words: 3 / 715
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My results are shown in the appendix. As you can see, ? always diverges to either positive or negative infinity. However, for E=1, the correct eigenvalue for n=0, you see all of the ‘interesting’ part of the wavefunction before it diverges, whereas for the other values of E the solution diverges before it reaches zero...


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I did this by trying successive values of E until one gave a solution that approached zero at about x1 is 4. This works because, as we saw for n=0, the values either side of the correct eigenvalue didn’t ever reach zero.

Conclusion

The numerical approach gives a very close approximation to the analytic solution for reasonable x, and with it you are also able to correctly find the eigenvalues for the first few states of the system, although you have to be able to start reasonably close to the eigenvalues to find the correct ones...


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