Scattering in the PT-symmetric Coulomb potential

Details Scattering in the PT-symmetric Coulomb potential Scattering in the PT-symmetric Coulomb potential

2009-06-11

arxiv.org/abs/0906.2092v1

2009 J. Phys. A: Math. Theor. 42 295201 (9pp)

Physics

Quantum Physics

Journal of Physics A: Mathematical and Theoretical 42 (2009) to appear

Scientific paper

10.1088/1751-8113/42/29/295201

Scattering on the ${\cal PT}$-symmetric Coulomb potential is studied along a U-shaped trajectory circumventing the origin in the complex $x$ plane from below. This trajectory reflects ${\cal PT}$ symmetry, sets the appropriate boundary conditions for bound states and also allows the restoration of the correct sign of the energy eigenvalues. Scattering states are composed from the two linearly independent solutions valid for non-integer values of the 2L parameter, which would correspond to the angular momentum in the usual Hermitian setting. Transmission and reflection coefficients are written in closed analytic form and it is shown that similarly to other ${\cal PT}$-symmetric scattering systems the latter exhibit handedness effect. Bound-state energies are recovered from the poles of the transmission coefficients.

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