论文标题
Green的schrödinger方程功能具有广义上的点相互作用和稳定性
Green's Function for the Schrödinger Equation with a Generalized Point Interaction and Stability of Superoscillations
论文作者
论文摘要
在本文中，我们研究了依赖时间的schrödinger方程，其中所有可能的自我接合奇异相互作用都位于原点，其中包括$δ$和$δ'$ - 电位以及Dirichlet，Neumann和Robin Type的边界条件（特定情况）。 我们使用菲涅尔积分来得出了依赖格林的函数的明确表示，并使用菲涅耳积分为相应的整体含义提供了数学上的严格含义。上震功能出现在量子力学中弱测量的背景下，自然被视为全体形态的整个功能。作为绿色函数的应用，我们研究了当初始基准是一种升级函数时，Schrödinger方程解的稳定性和振荡特性会受到广义点相互作用。
In this paper we study the time dependent Schrödinger equation with all possible self-adjoint singular interactions located at the origin, which include the $δ$ and $δ'$-potentials as well as boundary conditions of Dirichlet, Neumann, and Robin type as particular cases. We derive an explicit representation of the time dependent Green's function and give a mathematical rigorous meaning to the corresponding integral for holomorphic initial conditions, using Fresnel integrals. Superoscillatory functions appear in the context of weak measurements in quantum mechanics and are naturally treated as holomorphic entire functions. As an application of the Green's function we study the stability and oscillatory properties of the solution of the Schrödinger equation subject to a generalized point interaction when the initial datum is a superoscillatory function.
