Effects of Two Successive Parity-Invariant Point Interactions on One-Dimensional Quantum Transmission: Resonance Conditions for the Parameter Space

Abstract

We consider the scattering of a quantum particle by two independent, successive parity-invariant point interactions in one dimension. The parameter space for the two point interactions is given by the direct product of two tori, which is described by four parameters. By investigating the effects of the two point interactions on the transmission probability of plane wave, we obtain the conditions for the parameter space under which perfect resonant transmission occur. The resonance conditions are found to be described by symmetric and anti-symmetric relations between the parameters.

8 pages, 8 figures, minor revision

References in corpus (4)

• Two-point one-dimensional $\delta$-${\delta }^{\prime }$ interactions: non-abelian addition law and decoupling limit
• The Infinite Square Well with a Point Interaction: A Discussion on the Different Parametrizations
• Controlling a resonant transmission across the ${\delta }^{\prime }$-potential: the inverse problem
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Cited by in corpus (9)

• Families of one-point interactions resulting from the squeezing limit of the sum of two- and three-delta-like potentials
• Point interactions with bias potentials
• A phenomenon of splitting resonant-tunneling one-point interactions
• Resonant Transmission in One-Dimensional Quantum Mechanics with Two Independent Point Interactions: Full Parameter Analysis
• Scattering data and bound states of a squeezed double-layer structure
• Quantum Reflection and Transmission in Ring Systems with Double Y-Junctions: Occurrence of Perfect Reflection
• Origin of resonant tunneling through single-point barriers
• Bound States and Resonance Analysis of One-Dimensional Relativistic Parity-Symmetric Two Point Interactions
• Furcation of resonance sets for one-point interactions