Extended Schrödinger equation leading to squeezing phenomena

In a previous paper we showed that an extended Schrödinger equation (ESE) can lead to critical phenomena. The ESE was defined as an integro-differential Schrödinger equation obtained from the traditional differential Schrödinger equation by extending the local potential to a non-local potential. Here we pursue further this procedure by constructing a class of such ESE which is able to generate the (quantum) squeezing phenomenon. As an example, we discuss a model by Glauber for particle trapping by oscillating fields, in the present perspective.