The regulated four parameter one dimensional point interaction

Abstract

The general four parameter point interaction in one dimensional quantum mechanics is regulated. It allows the exact solution, but not the perturbative one. We conjecture that this is due to the interaction not being asymptotically free. We then propose a different breakup of unperturbed theory and interaction, which now is asymptotically free but leads to the same physics. The corresponding regulated potential can be solved both exactly and perturbatively, in agreement with the conjecture.

17 pages, no figures, Tex file

References in corpus (1)

• Four-Parameter Point-Interaction in 1-D Quantum Systems

Cited by in corpus (11)

• A Free Particle on a Circle with Point Interaction
• Symmetry, Duality and Anholonomy of Point Interactions in One Dimension
• Renormalized Path Integral for the Two-Dimensional Delta-Function Interaction
• Distribution theory for Schrödinger's integral equation
• Distributional approach to point interactions in one-dimensional quantum mechanics
• Spectral properties on a circle with a singularity
• Realization of a Four Parameter Family of Generalized One-Dimensional Contact Interactions by Three Nearby Delta Potentials with Renormalized Strengths
• Duality between weak and strong interactions in quantum gases
• Regularization of a strong-weak duality between pointlike interactions in one dimension
• Regularization of energy-dependent pointlike interactions in 1D quantum mechanics
• Bound States and Resonance Analysis of One-Dimensional Relativistic Parity-Symmetric Two Point Interactions