论文标题
$ \ mathbb {r} \ setMinus \ {0 \} $中schrödinger方程的超激动的时间演变
Time evolution of superoscillations for the Schrödinger equation in $\mathbb{R}\setminus\{0\}$
论文作者
论文摘要
在量子力学上的上升或更通用的超速度的背景下，作为时间依赖的schrödinger方程的初始条件。已经在\ cite {abcs21_2}中开发了一种统一的方法，该方法在某些全态性和增长假设下在相应的绿色函数上产生了超速度属性的时间持久性。尽管该理论考虑了整个真实行$ \ Mathbb {r} $上的Schrödinger方程，但本文采取了自然的下一步，并考虑了$ \ Mathbb {r} \ setMinus \ {0 \ {0 \} $，并允许在$ x = 0^\ pm $的边界条件下允许边界条件。特别是涵盖了单数$ \ frac {1} {x^2} $ - 涵盖了非常重要的$δ$和$Δ'$分布电位。
In the context of quantum mechanics superoscillations, or the more general supershifts, appear as initial conditions of the time dependent Schrödinger equation. Already in \cite{ABCS21_2} a unified approach was developed, which yields time persistence of the supershift property under certain holomorphicity and growth assumptions on the corresponding Green's function. While that theory considers the Schrödinger equation on the whole real line $\mathbb{R}$, this paper takes the natural next step and considers $\mathbb{R}\setminus\{0\}$ instead, and allow boundary conditions at $x=0^\pm$ in addition. In particular the singular $\frac{1}{x^2}$-potential as well as the very important $δ$ and $δ'$ distributional potentials are covered.
