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sometimes I see [\hat{q},\hat{p}] = i\hbar\widehat{\{q,p\}} + O(\hbar^2)
what does the last term O(\hbar^2) mean?
[tex]x=y[/tex]
what does the last term O(\hbar^2) mean?
[tex]x=y[/tex]
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Hurkyl said:It's asymptotic notation. Since you're probably in a context where everything's analytic... O(x^2) is essentially just shorthand for "possibly plus some more terms involving powers of x with exponent at least 2".
kakarukeys said:finally latex is back:
here's the equation that's puzzling me:
[tex][\hat{q},\hat{p}] = i\hbar\widehat{\{q,p\}} + O(\hbar^2)[/tex]
without [tex]O(\hbar^2)[/tex], the equation is just the usual canonical quantization recipe. what is that term for?
kakarukeys said:Read post#7 in the thread "transition from poisson brackets to ..." if you follow my derivation, you will be able to see where the [tex]O(\hbar^{2})[/tex] term comes from.
O(something) stands for "Of Order Of" that "something".
sam