Schrödinger is a frozen cat that appears in Imago Fine Arts in the Dionysus Park level of BioShock 2. This cat is located in the back part of the frozen gallery, in an ice pile to the left of the back room entrance. The "cat" is actually a regular Dead Cat model like the ones that can be found elsewhere in Rapture. However, when the player rests their cursor on the model the name "Schrödinger" appears (unlike all the other models that just say "Corpse").
This is a reference to Schrödinger's Cat; a thought experiment by the famous physicist Erwin Schrödinger who postulated theories about quantum entanglement. In this thought experiment a hypothetical cat is sealed in a chamber and after a certain period of time is either alive or dead, depending on an earlier random event. The Copenhagen interpretation of quantum mechanics implies that the cat is simultaneously alive and dead.
It is worthy to note that even though the cat appears frozen, it does not shatter; when whacked or shot, it bleeds, leaving its status inconclusive (just like Schrödinger's experiment).