arXiv subjects

Peter Schlosser

Publications and source records attributed to Peter Schlosser.

21 records · Page 2Linked to original sources

arXiv2020

Green's Function for the Schrödinger Equation with a Generalized Point Interaction and Stability of Superoscillations

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.

math.AP↗

arXiv2019

Schrödinger evolution of superoscillations with $δ$- and $δ'$-potentials

In this paper we study the time persistence of superoscillations as the initial data of the time dependent Schrödinger equation with $δ$- and $δ'$-potentials. It is shown that the sequence of solutions converges uniformly on compact sets, whenever the initial data converges in the topology of the entire function space $A_1(\mathbb{C})$. Convolution operators acting in this space are our main tool. In particular, a general result about the existence of such operators is proven. Moreover, we provide an explicit formula as well as the large time asymptotics for the time evolution of a plane wave under $δ$- and $δ'$-potentials.

math-ph↗

arXiv2018

Quasi boundary triples, self-adjoint extensions, and Robin Laplacians on the half-space

In this note self-adjoint extensions of symmetric operators are investigated by using the abstract technique of quasi boundary triples and their Weyl functions. The main result is an extension of Theorem 2.6 in [5] which provides sufficient conditions on the parameter in the boundary space to induce self-adjoint realizations. As an example self-adjoint Robin Laplacians on the half-space with boundary conditions involving an unbounded coefficient are considered.

math.SP↗