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Complex Classical Motion in Potentials with Poles and Turning Points
Author(s) -
Bender Carl M.,
Hook Daniel W.
Publication year - 2014
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12059
Subject(s) - attractor , turning point , classical mechanics , motion (physics) , work (physics) , point (geometry) , symmetry (geometry) , physics , trajectory , mathematics , mathematical analysis , geometry , quantum mechanics , acoustics , period (music)
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 toward 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.