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please help me solve problem 7, 8, 9, thanks.

5. Calculate $⟨m∣x∣n⟩$ and show that it vanishes unless $n=m±1$. 6. Calculate $⟨m∣p∣n⟩$. 118 Chapter 6 Operator Methods in Quantum Mechanics 7. Use the results of Problems 6 and 7 to calculate $⟨m∣px∣n⟩$ and $⟨m∣xp∣n⟩$. (Hint: Insert the unit operator 1 between the two operators, and use the form $1=∑_{k}∣k⟩⟨k∣$ In Problems 5-7 it is useful to express $x$ and $p$ in terms of $A$ and $A_{+}$ 8. Use the results of Problem 7 to calculate $⟨m∣[p,x]∣n⟩$. 9. Prove that $⟨n∣x∣n⟩$ and $⟨n∣p∣n⟩$ both vanish.

7. Using the hint and the results from Problems 5 and 6, we have:

Similarly,