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Physics
Atomic and Condensed Matter
Finite difference problem
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[QUOTE="soarce, post: 5475337, member: 116188"] Assuming that there is no error in your implementation you can perform a quick check: double the number of sample points simultaneously in x and y and see how the eigenvalues are shifting. As the energy is increasing the values should display a larger shift, in this way you can determine which values you should trust and which don't. For large energy values and wavefunctions of complex structure (nodes, angular momentum etc) one should increase the number of sample points (or decrease the spatial step h). This fact is due to the discretization of a continuous system, the eigenvalues you get are only approximate values or even spurious values (i.e. values which don't correspond to any eigenvalues of the continuous equation). In your case, for instance, the complex eigenvalues. The task of discriminating the spurious eigenvalues from physical ones is not trivial and requires some practice. I didn't work with finite diferences, but I came across this problem using spectral methods. I can recommend you the sections 7.5 and 7.6 from Boyd's book [URL='http://perso.uclouvain.be/alphonse.magnus/num1a/boyd01.pdf']Spectral metods [/URL]where he discuss some criteria for rejecting spurious and unphysical eigenvalues. Maybe they can help you. PS: other thing that you can do to minime the numerical errors is to take advantage of the symmetry of the equation, e.g. if you look for radial symmetric solutions then use polar coordinates instead of cartesian ones. [/QUOTE]
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Finite difference problem
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