This discussion investigates inverse eigenvalue solutions as creating a pattern that might fit numerical sequences or time series, with the solution providing a mathematical or physical model.
In particular, application of the inverse Sturm-Liouville Eigenproblem (iSLE) using the revisited Matrix-Variational Method [1], can be applied to time series analysis as suggested in RG by Jean-Philippe Montillet.
For example, if one could estimate a functional model with known signals within a time series, in the presence of complex noise (i.e. sum of white plus colored noise, or mix chaotic noise). Can we estimate this functional model as an iSLE, in those terms? This could be interesting, with many applications, including climate change.
As another example, it is possible to hear the shape of a drum [2]. The eigenvalues representing the possible modes of vibration, give a common basis for a certain shape, and not others. Noise in the measurement may also be reduced by using the eigenproblem itself to filter, processing only the part of the signal that correspond to viable oscillating shapes. The same can happen in quantum mechanics.
[1] Preprint On the Matrix-Variational Method (MVM) for Solving the Sturm...
[2] https://www.math.ucdavis.edu/~hunter/m207b/kac.pdf
This discussion is now closed. RG is unsuitable for physics discussions, for lack of moderator and presence of cabals. I can be reached by PM.
Kharbid,
Thank you. The MVM can be extended to finding potentially new quantum models in day-to-day occurrences such as numerical sequences and measurement of time series.
Many systems obey known numerical sequences, the question here is if there is a quantum model that fits the observation, and secondly, what, if any, insight can we get from such a physics model?
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http://faxi.org/community/forum/topic/3026
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