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## Main Question or Discussion Point

**Quantum Harmonic Oscillator Operator Commution (solved)**

**EDIT**

*This was solved thanks to CompuChip! The entire post is also not very interesting as it was a basic mistake :P No need to waste time*

This is not homework (I am not currently in college :P), but it is a mathematical question I'm stuck and I would

__greatly__appreciate help.

The Quantum harmonic oscillator Operator method uses:

[tex]\widehat{a}[/tex] = [tex]\sqrt{\frac{m\omega}{2\hbar}}[/tex]([tex]\widehat{x}[/tex] + [tex]\frac{i\widehat{p}}{m\omega}[/tex])

and

[tex]\widehat{a}[/tex][tex]^{+}[/tex] = [tex]\sqrt{\frac{m\omega}{2\hbar}}[/tex]([tex]\widehat{x}[/tex] - [tex]\frac{i\widehat{p}}{m\omega}[/tex])

It also says that:

[[tex]\widehat{a}[/tex],[tex]\widehat{a}[/tex][tex]^{+}[/tex]] = 1

[[tex]\widehat{a}[/tex],[tex]\widehat{a}[/tex][tex]^{+}[/tex]] = [tex]\widehat{a}[/tex][tex]\widehat{a}[/tex][tex]^{+}[/tex] - [tex]\widehat{a}[/tex][tex]^{+}[/tex][tex]\widehat{a}[/tex]

I keep ending up with 2!

Here is a

*"proof"*

http://quantummechanics.ucsd.edu/ph130a/130_notes/node169.html

But they have simply multiplied [tex]\widehat{a}[/tex][tex]\widehat{a}[/tex][tex]^{+}[/tex]

I feel like I cannot continue(self-study) until I see how I'm wrong. Please help!

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