Erwin Schrödinger doesn't appear to have personally owned a cat. He did however own a dog.

Is Schrödinger's cat a real cat?

"Schrodinger's Cat" was not a real experiment and therefore did not scientifically prove anything. Schrodinger's Cat is not even part of any scientific theory. ... In Schrodinger's imaginary experiment, you place a cat in a box with a tiny bit of radioactive substance.

What is Schrödinger cat called?

His name is Schrödinger. In Wild Arms 3, the character of Shady the Cat, owned by Maya Schrödinger, is based on Schrödinger's cat, and is claustrophobic as a result of the "experiment".