Abstract
Quantum delay time tomography data obtained from the intensity of a Gaussian wave packet are used to approximately construct the 3D scattering potential of the time dependent Schr\"odinger's equation by a least action tomography algorithm which decouples into multiple 2D x-ray tomography algorithms when the mean energy of the wave packet is sufficiently high. We obtain two ``miracle'' identities for the characterization of admissible quantum delay time tomography data. The first is related to Newton's miracle identity. The second is a new curved miracle identity.
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