Talk:Split-step method

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Sign of kinetic energy term

In the discussion of the physics application of the non-linear Schrodinger equation the kinetic propagation term is given as $e^{idtk^{2}}$ . From the association between real and Fourier space, ${\frac {\partial }{\partial x}}\leftrightarrow ik$ , I would expect that $e^{i{\frac {dt}{2}}{\frac {\partial ^{2}}{\partial x^{2}}}}\leftrightarrow e^{-ik^{2}dt/2}$ .

So it seems that there is a factor -1/2 missing here. But to be honest, I am quite confused because there appear to be a lot of different signs in the web. Could someone please check that and edit if necessary? Thanks! 2001:4BC9:B42:753A:1DC6:2ACD:70ED:87D0 (talk) 09:51, 1 December 2021 (UTC)[reply]