The concept of the self-function has already been "spended" in theoretical physics, for instance in the Schrödinger self-functions [SF] (as solutions of univocally formulated differential equations in describing the stationary quantum states of an electron in an atom or molecule) which, among other things, are expressions of conditions of stability of mechanically energetic intra-atomic, and so also of electronic, states, which [conditions of stability] only in extreme cases (for instance very high temperature together with thermic isolation) do transform the gross-qualitative atomic structure. Their simple summary does not result in an existential self-function [ESF]. The constituents of an atomic ESF -- if one thinks about such an analogue -- would practically be of a nuclear-physical nature.
In the mosaic-nuclear forms of composed molecules [a molecule may be viewed as an atom with more than one nucleus] we arrive at, albeit nucleus-induced but "residing" in the electron shells, states for which there are similar SF's [i.e. Schrödinger self-functions]. It is because of the fact that here the possible states are not only (merely lightly) influenced by their sister-electrons and their own nucleus, but moreover being influenced by more or many nuclei, that these states are already symbols of a complex molecular whole (Computationally things here cannot be exactly determined anymore, because on the one hand we here have to do with a many-body problem, and on the other it is about more subtle relationships than may be determined in the case in simple electrostatically electronic settings). These individual SF's are coupled with the others already in so strong a fashion allowing one to summarize things "behavioristically" and so resulting in an, albeit vague, analogue of the ESF. In the organism the ESF in turn is quite different, because we here have states which are at all possible only when two conditions are satisfied : 1. Atomic special form (= allomeric state of the organogeneous chemical elements) [Apparently it is meant here that in the case of organisms we have to do with (mega) molecules (the organisms themselves as to their essence) always containing all the organogeneous elements C, O, H, N. And these elements are not, as the chemical elements in all other (inorganismic) molecules, definitivey fixed as to their stoichiometrics, i.e. as to their proportion in the molecule]. 2. Fixation as to resonance in the mega-molecule [i.e. an overall resonance is demanded also in these mega-molecules]. A subdivision or classification into SF constituents is here [i.e. in organisms] not possible anymore (one may try it when one wants to) as if one could speak of an ESF.
A certain formal relationship existing between the organismic ESF an the Schrödinger SF [i.e. the Schrödinger wave-equation] becomes clear from the following consideration : If one wishes to recognize in Nature an overall functionalism -- the temptation to see such functionality in everything is great, and many authors again and again submit to it all the way down to atomic structure -- then one may do this without objection, if one identifies (good or bad) functionality with (good or bad) existence, and so not limiting existence to form diversity (to which one certainly might adhere), and taking every process to be a transition from -- seen in an overall conditional context -- less stable to more stable existence. In order not demonize the transitional process among different [degrees of] existences, and with it among different ESF's, i.e. not to base them onto a (here not useful) will-to-create, one may take the onset of such a transitional process to be a factor of proportionality of reciproke stability (in "reality" things are and remain of course the other way around, namely that to apply the familiar concept of stability to molecular systems is scientifically well-based in virtue of the specific values that can be assumed by the ESF's [what ESF is stable in the present condition?] ). One now has arrived at the "stability" only [i.e. one has now arrived at stability itself] which can immediately be connected with Being. And the nature of Being is so exhaustively discussed by the existential philosophers that we may leave it at this [We would like to add that instead of "existential philosophers", such as Sartre, it would be more appropriate to mention the metaphysics of Aristotle, where "to be" means having such and such a qualitative content guaranteeing internal stability and determining external stability or instability in different existential conditions. The ESF may be compared with Aristotle's formal cause in the thing. This formal cause, i.e. the what-is-it content, the form of the thing, exhibits something of the permanence and stability required by true Being.]. Because also the Schrödinger SF indicates, as probability of transition in electronic states, the recoproke value of the stability (temporary existence) of these states, there exists a, qua direction and "essence", similar relationship [as in the case of organismic ESF], at least not a disparateness.