Operator Transformation

$⟨\psi |{\hat{Q}}^{\prime }|\psi ⟩=⟨{\psi }^{\prime }|\hat{Q}|{\psi }^{\prime }⟩$

• How a transformation is defined

${\hat{Q}}^{\prime }={\hat{T}}^{†}\hat{Q}\hat{T}$

• ${\hat{Q}}^{\prime }$ refers to the transformed operator
• $\hat{T}$ is some transformation operator