QM4: The Hamiltonian of a harmonic oscillator is given by H = hw (a²a + 1² ) a) Prove that [H, at] hwat. (Show your work

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Qm4 The Hamiltonian Of A Harmonic Oscillator Is Given By H Hw A A 1 A Prove That H At Hwat Show Your Work 1 (184.13 KiB) Viewed 13 times

QM4: The Hamiltonian of a harmonic oscillator is given by H = hw (a²a + 1² ) a) Prove that [H, at] hwat. (Show your work, step by step!) b) Assume |E) is an eigenstate with the eigenenergy E. Use the result from (a) and show that the eigenenergy of state (a¹|E)) is given by E + ħw. (Show your work, step by step!) c) Calculate the following: (4|a|5), (6|a¹|5), (2|a¹a|2), (4|x|3) =