Can someone give me an example of a nonlinear operator? My textbooks always proves that some operator is a linear operator, but I don't think I really know what a nonlinear operator looks like.(adsbygoogle = window.adsbygoogle || []).push({});

One of my books defines an operator like [tex]\hat{B} \psi = \psi^2[/tex]. I see that this is a nonlinear operator because:

[tex]\hat{B} (\psi_1 + \psi_2) = (\psi_1 + \psi_2)^2[/tex]

...and this is different from [tex]\psi_1^2 + \psi_2^2[/tex] which you would get by letting the operator B act on each function. But how can you define an operator like this? What would the mathematical form of such an operator be?

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# Nonlinear operators

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