Abstract
A new sort of matter wave with the general astigmatism is proposed, whose orientation of the phase front and the density profile are crossed. A generalized ABCD law is developed to treat the evolution of the general astigmatic matter wave. It is revealed that two "cylindrical lens" pulses with oblique orientations can bring general astigmatism to the matter wave. The evolution characteristics of the general astigmatic matter wave in the gravitational field is discussed and illustrated numerically in detail. It is found that the orientations of the density profile and the phase front of the matter wave rotate continuously during evolution.
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