Word Count : 222

---

The Hamiltonian for a quantum harmonic oscillator is [ \hat{H} = \hbar \omega \left( \hat{a}^\dagger \hat{a} + \frac{1}{2} \right), ] where (\hat{a}) and (\hat{a}^\dagger) are the annihilation and creation operators, and ([\hat{a}, \hat{a}^\dagger] = 1). i) To show ([\hat{H}, \hat{a}] = -\hbar \omega \hat{a}): [ [\hat{H}, \hat{a}] = \left[ \hbar \omega \left( \hat{a}^\dagger \hat{a} + _____ ___ ___ _____ ___.
__________ ________ ________ _________ ___ _____ _________ _____ ________ ________ _______.
_______ _______ ________ ______ ____ _____ ____ __________ _____ __________ ________.
__________ _______ _____ ________ _________ ___ _____ __________ ________ ___ ________.
_________ _____ ________ ________ ________ _________ _______ __________ _______ ___.
_____ __________ ______ ______ ___ _______ ________ _____ ____ _______.
__________ ___ _________ _______ ___ __________ ____ _________ ______ ____ __________ __________.
_________ __________ ___ ___ ____ _______ __________.
________ ____ ________ _________ _______.
__________ ______ _____ _______ ____ _________ ________.
________ ________ ____ ________ ___ ________ __________ _____ _____ ___.
__________ ___ __________ _______ _________ ______ _______.
___ ______ ______ __________ _____ ___ ______.
_________ ___ ___ __________ _________.
________ ______ __________ ____ _____.
______ _______ ____ ____ ____ ___ _________ ___ __________ _______ ________ ___.
________ __________ ___ __________ __________ _________ _________ ________ ___ __________ ____.
_______ ____ ______ _____ _____ ______ ___ ____.
_________ __________ ________ _________ ________.
_____ ________ ______ _______ ______ ____ ____ ________.
Get Full Answer on WhatsApp