The aim of such paper is to explain in detail the foundations of quantum cognition and to evidence the manner in which our pioneering experiments on quantum interference in humans should be correctly interpreted in the framework of a correct quantum mechanical elaboration. Often, studies on quantum cognition are elaborated from some authors evidencing that presently we have empirical evidence that the application of quantum rules gives better results respect to classical ones. Consequently, such studies are delineated as empirical tentatives. It is not true. Quantum cognition is a scientific realization structured about robust quantum foundations and this is the reason because it gives such important results. Consequently, we discuss the esigence to correctly explain the foundations of this emerging discipline. In order to reach this objective we analyze the fundamental role of the abstract entity that is called quantum mechanical wave function. Soon after we describe the manner in which quantum operators must be entered in cognition studies by using the projectors that represent logic statements and thus relate directly our cognitive functions. We also discuss in detail the logical origins of quantum mechanics outlining that it does not represent a physical theory looking at the matter at microscopic level but a God Giano two faces looking simultaneously to material and to mental reality. We also discuss results establishing the nature of our consciousness and the unquestionable result that it obeys to the basic rules of quantum mechanics. We also give a further and pressing indication:that in quantum cognition studies the quantum wave function must be intended as reconstructed experimentally a posteriori in our cognitive studies and cannot be confused with the standard examining elaboration that is used in usual textbooks of quantum mechanics. Also the question of the order effect is analyzed in detail using the important notion of Reaction Time (RT)of psychology. In substance, we give a total reformulation of the current quantum cognition studies evidencing that previous elaborations finalized to present the corrent status of this discipline as empirical tentatives to characterize a quantum cognitive modelling result to be only approximate, uncorrect and confusing prospects that damage the information about the robust structure of quantum cognition and therefore need to be rejected.