Schrödinger is a cat, given as a gift to Narim by Carter. He is named for physicist Erwin Schrödinger who theorized that a cat in a box with a can of poison gas activated by the decay of a radioactive atom would simultaneously be both dead and alive.
Narim took Schrödinger with him to his new home on Tollana, and he later sent the cat back to Earth using phase-shift technology that would allow it to pass through the closed iris as a signal of a friendly communication from the Tollans. Schrödinger returned with Narim to Tollana.
Cross Reference: Narim, Tollana, Tollans
Episode Reference: Enigma, Pretense