I will introduce two types of unique continuation properties for the linear higher order Schrödinger equations.

The first type concerns unique continuation through global non-characteristic hyperplanes. I will start by reviewing some classical local theories, ideas of which may look far away from higher order evolution operators. The motivation of proving a global result comes from its possible application in non-linear problems, which was studied by Kenig, Ponce, Vega and Ionescu.

The second type is quantitative. Escauriaza, Kenig, Ponce and Vega have earlier found that the Hardy’s uncertainty principle has a direct relation to a unique continuation property for Schrödinger equations. I will introduce a result in this aspect for the higher order Schrödinger equations in one spatial dimension, and show its sharpness by examples.