On survival probability of quantum states

The survival probability of a quantum state encodes essential information concerning the decay rate of quantum particles and is the primary object for investigating the time-energy uncertainty relations and the occurrence of the quantum Zeno effect. The purpose of this article is to uncover some curious properties concerning the relations between the values of the survival probability of a quantum state at different times. These relations put surprising restrictions on the evolution pictures of quantum states, and also illustrate their peculiar intricacies.