# Unique continuation properties for Schroedinger operators in Hilbert spaces

## TL;DR

This paper establishes unique continuation properties and uncertainty principles for abstract Schrödinger equations with time-dependent potentials in Hilbert spaces, broadening understanding of their behavior in various physical systems.

## Contribution

It introduces a general framework for unique continuation in Hilbert space valued Schrödinger equations, applicable to diverse physical models.

## Key findings

- Derived Morgan type uncertainty principles.
- Established unique continuation properties for abstract Schrödinger equations.
- Applicable to a wide range of physical systems.

## Abstract

Here, the Morgan type uncertainty principle and unique continuation properties of abstract Schredinger equations with time dependent potentials are obtained in Hilbert space valued function classes. The equations include linear operator in abstract Hilbert spaces H dependent on space variables. So, by selecting appropriate spaces H and operators, we derive unique continuation properties for numerous classes of Schr\"odinger type equations and its systems, which occur in a wide variety of physical systems.