I have a homework problem which asks me to compute the second and third excited states of the harmonic oscillator. The function we must compute involves taking the ladder operator to the n-power. My question is this: because the ladder operator appears as so, -ip + mwx, and because I am using it as a differential operator, is it ok to move the x around as I see fit? For example, when the ladder operator is squared, I get cross terms which contain x and d/dx. Am I able to move the x outside of the d/dx, in which case it will appear as 2(hbar)mwx(d/dx), or will I have one cross term which reads (hbar)(d/dx)mwx and the other which reads mwx(hbar)(d/dx)? (minus signs ignored)(adsbygoogle = window.adsbygoogle || []).push({});

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# Ladder operators homework

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