Talk:Split-step method

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 $$e^{i dt k^2}$$. From the association between real and Fourier space, $$\frac{\partial}{\partial x} \leftrightarrow i k $$, I would expect that $$e^{i \frac{dt}{2} \frac{\partial^2}{\partial x^2}} \leftrightarrow e^{- i k^2 dt/2}$$.

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)