I am working on the topic of optimal control in NMR, where spins undergo non-unitary evolution caused by gradient field pulses at different time intervals. I am studying the effects of this on the spin dynamics.
For my project I need a particular kind of gradient field as given by the equation $-z\exp(-z^2)$, where $z$ is the the spatial position of the region from center of the sample. All the books I had referred to (Levitt's Spin Dynamics and Keeler's Understanding NMR Spectroscopy) talk about constant gradients. So I have no idea if it is possible to create even an approximation of a spatially varying gradient as given here.
In particular, I need my field due to the gradient to look like a delta function in space. So I thought of using a derivative of a Gaussian with a small standard deviation as an approximation, which is the equation given above.