The Hamiltonian for the one dimensional quantum oscillator is 1 Н p² 1 + 2m 2 +mw²x² 2m where k = mw² 1) Define the operators ₁₁ and ₁₁ such that Ĥ = ½ħw(p² + î²). Define Ĥ₂ a a function of 1 and ₁ such that Ĥ = ħwĤ₂. - 2) Let us define the new operators â = 1/2(1 + iĝ₁) and ↠= ½(î₁ — iŷ1).
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