Scattering in the PT-symmetric Coulomb potential

Abstract

Scattering on the $\mathcal{P}\mathcal{T}$-symmetric Coulomb potential is studied along a U-shaped trajectory circumventing the origin in the complex $x$ plane from below. This trajectory reflects $\mathcal{P}\mathcal{T}$ 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 $\mathcal{P}\mathcal{T}$-symmetric scattering systems the latter exhibit handedness effect. Bound-state energies are recovered from the poles of the transmission coefficients.

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

References in corpus (2)

• Making Sense of Non-Hermitian Hamiltonians
• Asymptotically vanishing PT-symmetric potentials and negative-mass Schroedinger equations

Cited by in corpus (1)

• Scattering theory using smeared non-Hermitian potentials