Schrödinger was Captain Samantha Carter's pet cat, named after the 20th century physicist Erwin Schrödinger and his thought experiment in Quantum Physics, known as Schrödinger's cat.
During the Tollans' forced stay at Stargate Command, Carter gave the cat to Narim, who displayed certain curiosity, as animals had been long extinct on his homeworld. (SG1: "Enigma")
Two years later, when the Tollans contacted the SGC again to invite SG-1 to the Triad involving Skaara and Klorel, they sent Schrödinger through the Stargate first. Thanks to Tollan technology, the cat passed through the Iris unharmed and was reunited with Carter. (SG1: "Pretense")