The raising (a") and lowing (a) operators associated with a simple harmonic oscillatorHamiltonian (H) are given byax-ißpax+ißpaawhere a and B are real constants with aß1and [x.p] = i .(a) Show that the commutator a", a*] = a a* - a*a = 1(b) Show that the commutator [H,a*] = ħoa+(c) Using the identity obtained in (b), show that a"yn) is an eigen state of H with eigenenergy ho n+1+-21Helpful equations: H = ħo a*aa*a |Vn) = n\Wn}

(a) The commutator of the lowering and raising operators is calculated in the following way.

Answered: The raising (a) and lowing (a)…

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