He is a Junior Warrant Officer serving in the Millennium military unit of Werewolf, and was created by Doc. He takes the form of a young boy, with cat ears and a perpetual smirk, dressing in a Hitler Youth uniform and holding the rank of Oberstammführer (Warrant officer). In the Hellsing Ultimate OVA series, Schrödinger can be seen to have a tail when Doc tells him he can look at the Captain's guidebook, Though previously in the same scene he is shown to not have one and this is therefore normally associated to be a reference to the Captains werewolf characteristics. Usually found sitting near the Major's throne like a pet, he also acts as an envoy for Millennium. Due to his ability to be "everywhere and nowhere" at the same time, he has proved to be a useful spy and messenger for Millennium's forces.
Schrödinger first appears in OVA 4, showing up out of nowhere in the conference between Hellsing, the Queen, and Iscariot. He delivers a message from The Major on a two-way hand held television, declaring war on England and Alucard. After he finishes, Integra orders Alucard to kill Schrödinger, blasting his head off point-blank. His body disappears soon after when no one was looking. He turns up in the command center of the Deus Ex Machina, apparently unscathed, commenting how the Major should try to lose weight, as he could travel half way around the world, have his head blown off, and come back there in the time it took for the Major to walk down a hallway.
In the same episode, he appears again on the deck of the British ship Eagle in order to deliver another message from The Major via two-way hand held television to a defeated Rip van Winkle, saying "Auf Wiedersehen." with the other troops as Alucard devoured her. His next appearance is in OVA 7, showing up in the remnants of Seras Victoria and Pip Bernadotte's memories to inform Zorin Blitz that Doc and The Major got their hands on a "new toy" (Walter) and are unable to attend to incinerating Zorin. He then bids her farewell, leaving her to be killed by a deranged Seras. He then shows up on the bridge of the Deus Ex with the Major overlooking the scorched and wartorn London, commenting, with a smile, on how his only concern is for destruction and warfare, gladly dragging his allies down to hell with him.
In chapter 77 Finesthour 2, he greets Sir Integra and Seras as they enter the landed Hindenburg II, making the mistake of continuing to call Integra "Fräulein" after the Major stopped doing so as a sign of respect (in the beginning of episode one of the OVA, Integra's uncle Richard, in the English dub, had referred to Integra as "Fräulein" when he tried to kill the girl). Integra then swiftly blows off his head (again) with her handgun. Due to his abilities he survives this blow, turning up in chapter 84 Warcraft 2.
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, and by extension neither can Alucard, the one who has absorbed him. Whilst neither are technically dead, they do not exist in one place because they cannot recognize themselves, and have thus become "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. Yet, Alucard manages, in the end after 30 years, to return; Alucard kills off the 3 millions plus souls that reside in him so he can recognize himself. In doing so, it appears that he gained Schrödinger's powers, as shown by the fact that he appeared out of nowhere in Integra's bedroom and was perfectly fine after not having drank any blood for 30 years. Before this, a span of twenty years without blood reduced him to a corpse-like state. Presumably Schrödinger's soul is still within Alucard, as he mentions that he killed everyone except one and says "and now I am everywhere and nowhere"; implying he now has full access to Schördinger's abilities.
Powers and Abilities
The exact nature of Schrödinger's abilities has yet to be defined, although they are indirectly confirmed by the Major - he states that Schrödinger only exists for as long as he is aware of himself. He was able to appear in Hellsing's conference room without difficulty, despite the high security of the building at the time. He also appeared to Zorin Blitz while Blitz was attempting to attack Seras Victoria's mind, indicating that he can appear in mental realms as well. Schrödinger himself often states that he is "everywhere and nowhere", possibly meaning that, if he believes that he exists somewhere, then he will. In essence, his powers can be summed up as 'I think, therefore I am'. This also explains his apparent regeneration/immortality. If he believes that he is unscathed, then he is.