Dear Experts,

I am having difficulty undersanding the pattern when working with operators which is part of the work to evaluate <x^2>. See attached jpg.

Likewise the same with evaluating $\displaystyle a_{+}a_{-}\psi_{n}(x)$

Thanks

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- Nov 13th 2010, 01:06 PMbugatti79Harmonic Oscillator Finding <x^2>
Dear Experts,

I am having difficulty undersanding the pattern when working with operators which is part of the work to evaluate <x^2>. See attached jpg.

Likewise the same with evaluating $\displaystyle a_{+}a_{-}\psi_{n}(x)$

Thanks - Nov 13th 2010, 02:23 PMmr fantastic
- Nov 14th 2010, 01:56 AMbugatti79
On that basis,

I calculate $\displaystyle a_{+}a_{-} \psi_{n}=\sqrt{n} a_{+} \psi_{n-1}=\sqrt{n} \sqrt{n+1} \psi_{n}$

$\displaystyle a_{-} a_{+}\psi_{n}=\sqrt{n+1} a_{-} \psi_{n+1}=\sqrt{n+1} \sqrt{n} \psi_{n}$

$\displaystyle a_{-}^2 \psi_{n}=\sqrt{n} a_{-} \psi_{n-1}=\sqrt{n} \sqrt{n-1} \psi_{n-2}$

The first 2 calculations are wrong by my lectures notes, so obviously dont understand the definition.

For example, it there is an adding operator, I will sum it with n. Ie, adding a_+ operator to n+1 gives n+2, subtracting a_- to n gives n-1 etc..... - Nov 14th 2010, 09:58 AMmr fantastic
- Nov 14th 2010, 11:25 AMbugatti79