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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.
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?
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?