Towards Modelling QFT in Real Metamaterials: Singular Potentials and Self-Adjoint Extensions

Quantum Fest 2016 International Conference on Quantum Phenomena, Quantum Control and Quantum Optics

Nieto, L.M.^1 ; Gadella, M.^1 ; Mateos Guilarte, J.^2 ; Muñoz-Castañeda, J.M.^3 ; Romaniega, C.^1,4

Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, Spain^1

Departamento de Física Fundamental, Universidad de Salamanca, Spain^2

Departamento de Física ETSIAE, Universidad de Politécnica de Madrid, Spain^3

Departamento de Física Teórica II, Universidad de Complutense de Madrid, Spain^4

关键词: Dinger equation;    Point interactions;    Regular lattice;    Self-adjoint extensions;    Singular potentials;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/839/1/012007/pdf
DOI  :  10.1088/1742-6596/839/1/012007

来源: IOP

【 摘 要 】

Solutions of the one-dimensional Schrödinger equation are found when point interactions of the type aδ(x - q) + bδ′(x - q) are placed either in a couple of points or in a regular lattice. The results obtained in the present study are a first step toward a rigorous mathematical model of real metamaterials is Solid State Physics.