What do we mean by saying a cat in a box in schrodinger equation

Saying "a cat in a box" in the context of Schrödinger's equation is a reference to a thought experiment proposed by physicist Erwin Schrödinger in 1935. In this thought experiment, a cat is placed in a sealed box along with a radioactive substance that has a 50% chance of decaying and releasing a deadly poison that would kill the cat. According to quantum mechanics, the radioactive substance is in a superposition of both decaying and not decaying until it is observed. This means that until the box is opened and the cat is observed, it is theoretically both alive and dead at the same time.

This thought experiment was a way for Schrödinger to illustrate the concept of superposition and the strange implications of quantum mechanics on the macroscopic world. It highlights the idea that particles can exist in multiple states simultaneously until they are observed or measured, at which point they "collapse" into a single state.