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

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• Behavior of eigenvalues in a region of broken-PT symmetry
• The Quantum Effective Mass Hamilton-Jacobi Problem
• Schroedinger equations with indefinite effective mass
• Absence of Floquet scattering in oscillating non-Hermitian potential wells
• Quantum star-graph analogues of PT-symmetric square wells. II: Spectra
• CPT-conserved effective mass Hamiltonians through first and higher order charge operator C in a supersymmetric framework
• Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry
• Markov constant and quantum instabilities
• Lax-Phillips scattering theory for PT-symmetric ρ-perturbed operators
• Coulomb potential and the paradoxes of PT-symmetrization