When solving problems, particularly in optics, it is often that we represent the wave-function as a complex number, and then take the real part of it to be the final solution, after we do our analysis.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]u(\vec{r},t)=Re\{U(\vec{r},t)\}=\frac{1}{2}\left(U+U^*\right)[/tex]

HereUis the complex form of the wave function.

What my question is, is whether there exists some analyses regarding the validity of this approach. In general, can we prove that any of the operations we perform in the "complex domain" do not add "extras" to the real function, after we convert back.

Thanks in advance!

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# I Complex representation of wave function

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