# Two Non-Interacting Systems

## Prompt

“How many eigenstates does the combined system have?”

## Context

This SWBQ introduces two non-interacting identical systems with $N$ eigenstates each, and asks students to determine whether the new system will be extensive or intensive.

Students answer $N$ or $2N$. Using spin 1 system, ask for what the eigenstates of two spin-1 particles are. Soon we realize that it's $N^{(2)}=N^2$, which means it's neither extensive nor intensive.

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