Finding an annihilator operator

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To find an annihilator operator for (cosx)^2, the user initially calculated the first, second, and third derivatives, noting challenges with the resulting terms. They considered the operator D^2 + 2 but were hindered by the presence of the 2(sinx)^2 term. A suggestion was made regarding the operator D^3 + 4*D, which ultimately clarified the solution. The user recognized the oversight and expressed gratitude for the assistance. The discussion highlights the process of deriving an appropriate annihilator operator through derivative calculations.
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Homework Statement


Find an annihilator operator for (cosx)^2


Homework Equations





The Attempt at a Solution


first derivative -2cosxsinx
second derivative 2(sinx)^2 - 2(cosx)^2
third derivative 4sinxcosx +4cosxsinx

This isn't getting me anywhere (D^2 + 2) is close but I still have the 2(sinx)^2 term.

Any suggestions?
 
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What's wrong with (D^3+4*D)? It's staring you in the face.
 
Of course! I see it now. Thanks.
 

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