1. **State the problem:** We want to show that $$Q = \left(\frac{\partial}{\partial t} - \frac{H}{\hbar}\right)\Psi$$ where $\Psi$ is a wavefunction, $H$ is the Hamiltonian operator, and $\hbar$ is the reduced Planck constant. 2. **Recall the Schrödinger equation:** The time-dependent Schrödinger equation is given by $$i\hbar \frac{\partial \Psi}{\partial t} = H \Psi$$ This relates the time derivative of the wavefunction to the Hamiltonian acting on the wavefunction. 3. **Rewrite the Schrödinger equation:** Divide both sides by $i\hbar$: $$\frac{\partial \Psi}{\partial t} = \frac{1}{i\hbar} H \Psi$$ 4. **Express $Q$ in terms of $\Psi$:** Substitute the above into the expression for $Q$: $$Q = \left(\frac{\partial}{\partial t} - \frac{H}{\hbar}\right) \Psi = \frac{\partial \Psi}{\partial t} - \frac{H}{\hbar} \Psi$$ 5. **Use the Schrödinger equation substitution:** Replace $\frac{\partial \Psi}{\partial t}$ with $\frac{1}{i\hbar} H \Psi$: $$Q = \frac{1}{i\hbar} H \Psi - \frac{H}{\hbar} \Psi = \left(\frac{1}{i\hbar} - \frac{1}{\hbar}\right) H \Psi$$ 6. **Simplify the coefficient:** $$\frac{1}{i\hbar} - \frac{1}{\hbar} = \frac{1 - i}{i\hbar}$$ 7. **Interpretation:** The expression $Q$ is a linear combination of $H \Psi$ with complex coefficients. The exact form depends on the context, but this shows how $Q$ relates to the time derivative and Hamiltonian acting on $\Psi$. **Final answer:** $$Q = \left(\frac{\partial}{\partial t} - \frac{H}{\hbar}\right) \Psi = \left(\frac{1}{i\hbar} - \frac{1}{\hbar}\right) H \Psi$$