In chapter 87, Wolffang 2, Schrödinger appears again. He smiles maniacally and decapitates himself with an SS knife with the words inscribed into it "Meine Ehre heißt Treue" or "My honor is loyalty," the slogan of the SS. His body then falls into the blood that Alucard is drawing and absorbing into himself. Schrödinger was in fact the "poison" that the Major spoke of in chapter 84, Warcraft 2.
As Alucard's eyes close, Integra demands that the Major explains what is happening. The Major says that Schrödinger "carried the will of the self-observing Schrödinger's Cat" and "as long as he recognizes himself, he's everywhere and nowhere." But now that he is consumed by Alucard and is mixed with millions of other minds, he can no longer recognize himself. Schrödinger is no longer present anywhere, and thus also Alucard. The Major says that by now Alucard is "no more than a set of imaginary numbers."
Alucard seems to recognize his defeat, says farewell to Integra, and seems to disappear into thin air, leaving only the bloody Hellsing-pentagram on the ground, possibly symbolizing him being sealed away once again.