I'm having trouble figuring out why an equation simplifies the way it does.(adsbygoogle = window.adsbygoogle || []).push({});

(x and p refer to x hat and p_{x}hat, h refers to h bar, and the momentum operator is h/i dψ/dx )

I want to show that xpψ - pxψ = -h/i ψ

I understand that xpψ= x χ h/i dψ/dx

And pxψ= h/i x dψ/dx

When you try to simplify the subtraction expression you get:

x [itex]\times[/itex] h/i dψ/dx - h/i ψ - h/i x dψ/dx

The first and last part cancel out (do they?) to give the middle, -h/i ψ as the correct final answer.

But I don't get why they cancel, if that is what they are indeed doing. Is x χ (something) the same as (something) multiplied by x? If they are the same, then why don't they commute? In xpψ, you are calculating the effect of p on ψ followed by multiplication. In pxψ you are calculating the effect of multiplication by x followed by the effect of p.

But then when you are subtracting them to find the commutor, you can suddenly treat the order as irrelevant and cancel stuff out? Or am I misunderstanding how they got the final result?

(sorry if my notations are confusing, I'll work on learning how to write equations if no one knows what I am saying, this is just the commutation relation of position and momentum)

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# Operators and commutors, and order.

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