(Solved): please help me solve problem 7, 8, 9, thanks. 5. Calculate mxn and show that it van ...

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

5. Calculate $⟨m|x|n⟩$ and show that it vanishes unless $n=m\pm 1$. 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 $1={\sum }_k|k⟩⟨k|$ 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.