Quantum observable

An operator $\hat{f}$ on the Quantum Hilbert Space corresponding to a Classical observable $f$, as per the Postulate 2 of Quantum Mechanics, where

• $\mathcal{H}$ is the Quantum Hilbert Space
• $f:{\mathbb{R}}^{2n}\to \mathbb{R}$ is a Classical observable
• $\hat{f}:\mathcal{H}\to \mathbb{R}$ is the corresponding Quantum observable

The act of generating Quantum observable from Classical observable is known as Quantization.

Properties

• Eigenstate measurements are deterministic