Define what it means for an operator $Q$ to be hermitian and briefly explain the significance of this definition in quantum mechanics.

Define the uncertainty $(\Delta Q)_{\psi}$ of $Q$ in a state $\psi$. If $P$ is also a hermitian operator, show by considering the state $(Q+i \lambda P) \psi$, where $\lambda$ is a real number, that

$$\left\langle Q^{2}\right\rangle_{\psi}\left\langle P^{2}\right\rangle_{\psi} \geqslant \frac{1}{4}\left|\langle i[Q, P]\rangle_{\psi}\right|^{2}$$

Hence deduce that

$$(\Delta Q)_{\psi}(\Delta P)_{\psi} \geqslant \frac{1}{2}\left|\langle i[Q, P]\rangle_{\psi}\right|$$

Give a physical interpretation of this result.