Imaginary cubic oscillator and its square-well approximations in x- and p-representation

Details Imaginary cubic oscillator and its square-well approximations in x- and p-representation Imaginary cubic oscillator and its square-well approximations in x- and p-representation

2001-01-24

arxiv.org/abs/math-ph/0101027v2

in P. Milosav and I. Ercegovaca (editors), Mathematics and Mathematical Logic: New Research (Nova Publishers, 2009), pp.243-26

Physics

Mathematical Physics

17 pages, 7 figures

Scientific paper

Schroedinger equation with imaginary PT-symmetric potential $V^{}(x) = i\,x^3$ is studied using the numerical discretization methods in both the coordinate and momentum representations. In the former case our results confirm that the model generates an infinite number of bound states with real energies. In the latter case the differential equation is of the third order and a square-well, solvable approximation of kinetic energy is recommended and discussed. One finds that in the strong-coupling limit, the exact PT-symmetric solutions converge to their Hermitian predecessors.

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