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Inverse eigenvalue problems: reconstructing fractal potentials from eigenvalue spectra

Posted 21 days ago

The plot highlights the relationship between the shape of the potential and the corresponding wavefunctions. Inverse eigenvalue problems.

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POSTED BY: Michael Trott
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POSTED BY: EDITORIAL BOARD

The potential looks much nicer, when you plot the inverses of the primes. You get one more oscillation for every new prime. So one can anticipate an asymptotically oscillating potential that encodes all the information about primes. Pretty interesting.

V = dressingTransformationPotentials[1/# & /@ Prime[Range[50]], 400];
Plot[V[Abs[x]], {x, -400, 400}]

enter image description here

POSTED BY: Johannes Martin
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