Resonant Transmission in One-Dimensional Quantum Mechanics with Two Independent Point Interactions: Full Parameter Analysis

Abstract

We discuss the scattering of a quantum particle by two independent successive point interactions in one dimension. The parameter space for two point interactions is given by $U(2)\times U(2)$, which is described by eight real parameters. We perform an analysis of perfect resonant transmission on the whole parameter space. By investigating the effects of the two point interactions on the scattering matrix of plane wave, we find the condition under which perfect resonant transmission occurs. We also provide the physical interpretation of the resonance condition.

arXiv comment24 pages, 9 figures, minor revision

References in corpus (17)

• Fermion-Boson Duality of One-dimensional Quantum Particles with Generalized Contact Interaction
• Symmetry, Duality and Anholonomy of Point Interactions in One Dimension
• Boundary conditions for the states with resonant tunnelling across the ${\delta }^{\prime }$-potential
• Moebius Structure of the Spectral Space of Schroedinger Operators with Point Interaction
• Double Spiral Energy Surface in One-dimensional Quantum Mechanics of Generalized Pointlike Potentials
• Green functions for generalized point interactions in 1D: A scattering approach
• Two-point one-dimensional $\delta$-${\delta }^{\prime }$ interactions: non-abelian addition law and decoupling limit
• Supersymmetry in quantum mechanics with point interactions
• Supersymmetry and discrete transformations on S^1 with point singularities
• Duality and Anholonomy in Quantum Mechanics of 1D Contact Interactions
• Irregular Dynamics in a Solvable One-Dimensional Quantum Graph
• Extended supersymmetry and its reduction on a circle with point singularities
• Single point potentials with total resonant tunneling
• Supersymmetric Quantum Mechanics with a Point Singularity
• Supersymmetric Quantum Mechanics under Point Singularities
• Effects of Two Successive Parity-Invariant Point Interactions on One-Dimensional Quantum Transmission: Resonance Conditions for the Parameter Space
• Non-Abelian Monopole in the Parameter Space of Point-like Interactions

Cited by in corpus (6)

• Point interactions with bias potentials
• A phenomenon of splitting resonant-tunneling one-point interactions
• 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