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arXiv · 1402.3852

Complex classical motion in potentials with poles and turning points

Carl M. Bender·Daniel W. Hook
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Abstract

Complex trajectories for Hamiltonians of the form H=p^n+V(x) are studied. For n=2 time-reversal symmetry prevents trajectories from crossing. However, for n>2 trajectories may indeed cross, and as a result, the complex trajectories for such Hamiltonians have a rich and elaborate structure. In past work on complex classical trajectories it has been observed that turning points act as attractors; they pull on complex trajectories and make them veer towards the turning point. In this paper it is shown that the poles of V(x) have the opposite effect --- they deflect and repel trajectories. Moreover, poles shield and screen the effect of turning points.

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Carl M. Bender, Daniel W. Hook. 2014-02-16. Complex classical motion in potentials with poles and turning points. https://arxiv.org/abs/1402.3852

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