Non-catastrophic resonant states in one dimensional scattering from a rising exponential potential

2014/08/11 by Zafar Ahmed, Ahmed, Zafar, Lakshmi Prakash +3
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum and electron transport phenomena

paper · pdf · doi:10.48550/arxiv.1408.2367

openalex publication_date 2014/08/11 · openalex created_date 2016/10/28 · openalex updated_date 2026/07/28

Abstract

Investigation of scattering from rising potentials has just begun, these unorthodox potentials have earlier gone unexplored. Here, we obtain reflection amplitude (r(E)) for scattering from a two-piece rising exponential potential: V(x≤ 0)=V₁[1-e^-2x/a], V(x > 0)=V₂[e^2x/b-1], where V_1,2>0. This potential is repulsive and rising for x>0; it is attractive and diverging (to -∞) for x<0. The complex energy poles (\cal E_n= E_n-iΓ_n/2, Γ_n>0) of r(E) manifest as resonances. Wigner's reflection time-delay displays peaks at energies E(≈ E_n) but the eigenstates do not show spatial catastrophe for E=\cal E_n.

Related

• One dimensional scattering from two-piece rising potentials: a new avenue of resonances
• Outgoing solutions via Gevrey-2 properties
• Remarks to the Resonance-Decay Problem in Quantum Mechanics from a mathematical point of view
• Quantum Mechanical Reflection Resonances
• Scattering resonances for highly oscillatory potentials