---
tag: 9ZB5V94GPF
kind: statement
role: proposition
name: Addition Formula
sources:
  - wikipedia: en:4120642@r1338508195
    locator: Q-exponential, section Properties > Addition Formula
    note: adopted
    mention: wikipedia://en/4120642#V434
    sections: [Statement]
inventory: [NSP3GY86KG]
---

## Statement

The analogue of $\exp(x)\exp(y)=\exp(x+y)$ does not hold for real numbers $x$ and $y$. However, if these are operators satisfying the commutation relation $xy=qyx$, then $e_q(x)e_q(y)=e_q(x+y)$ holds true.