Suppose I have some observables [itex] \alpha, \beta, \gamma[/itex] whose central values and uncertainties [itex]\sigma_{\alpha}, \sigma_{\beta}, \sigma_{\gamma} [/itex] are known.(adsbygoogle = window.adsbygoogle || []).push({});

Define a function [itex] f(\alpha, \beta, \gamma)[/itex] which has both real and complex parts. How do I do standard error propagation when imaginary numbers are involved? This problem deals with the eigenvalues of a coupled oscillator. Here, some of the eigenvalue functions are complex, so I would like to know how to calculate the uncertainty on f, which is an eigenvalue. The claim is that since coupled oscillators are physical systems, their answers are real in nature. Thus, should I use [itex] Re(f) [/itex] instead?

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# A Uncertainty Propagation of Complex Functions

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