Shrodenger posses quantum reality manipulation powers. Basically "I think, therefore I am" and "I am everywhere, and nowhere" are the only two specific sets of parameters we have for Shordenger. And with that, basic logic, and feats from the manga. Yes Shrodenger was omnipresent. And thus, after absorbing and making it his own. Alucard is now omnipresent, and TRULY immortal from that. Before he wasnt exactly immortal in that the souls from 300million+ ppl he had absorbed gave him a form of psuedo imortality. But because he absorbs souls through his blood, when shrodenger sacrificed himself to "defeat" alucard, at the end of the battle of london, by sliting his throat and allowing himself to be absorbed by alucard, he used his "I think, therefore I am" clause to give individuality to all 300million+ souls. In order for Alucard to "come back" he had to battle them all, including shrodenger, taking 50+years to do so, and re-absorb their souls. If he was unable to defeat Shro and make his powers his own, he would never have been able to come back. Its kinda a catch, Shro was immortal but somehow Alucard "killed him" and absorbed his soul, and now hes "unkillable". I suppose its the "I think therefore I am" clause, basically the nigh instantaneous second between the moment when alucard blew Shros brains out, and the metabolic and enzymatic and neurological functions ceasing, eg "death" is what allowed shrodenger to be "immortal" by "thinking" hes not dead, before he dies. However with Alucards original psuedo imortality added to shrodengers own, sort of negates this effect as there are just too many souls within Alucard for this to happen as it's more than likely he keeps one or two souls that are constantly "thinking" hes not dead 24/7.