= Uniform half-line Schrodinger representation by boundary lifting
{title2=$q=g(t)e^{-x}+w$}
For the <free Schrodinger equation> with compatible smooth initial and boundary data, subtract $g(t)e^{-x}$ before taking a <Fourier sine transform>. The lifted initial datum vanishes at the endpoint, making its sine transform $O(k^{-2})$ if its second derivative is integrable. The transformed forcing is $k(ig-g')/(1+k^2)$; time integration followed by <integration by parts> makes its solution contribution uniformly $O(k^{-3})$. An integrable spectral majorant proves <uniform convergence> even at the compatible initial-boundary corner.
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