# Morgan type uncertainty principle and unique continuation properties for abstract Schr\"odinger equations

## TL;DR

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

## Contribution

It introduces new uncertainty principles and unique continuation results for abstract Schrödinger equations with operators in Hilbert spaces, applicable to many physical models.

## Key findings

- Derived Morgan type uncertainty principles for abstract Schrödinger equations.
- Proved unique continuation properties for a wide class of Schrödinger systems.
- Applicable to various physical systems with time-dependent potentials.

## Abstract

In this paper, Morgan type uncertainty principle and unique continuation properties of abstract Schr\"odinger equations with time dependent potentials in vector-valued classes are obtained. The equation involves a possible linear operators considered in the Hilbert spaces. So, by choosing the corresponding spaces H and operators we derived unique continuation properties for numerous classes of Schr\"odinger type equations and its systems which occur in a wide variety of physical systems