Derivation of Uncertainty Princple

[ChrisLM]

Referrence to Modern Quantum Mechanics, J.J.Sakurai,
I found the "Generalized Uncertainty Principle" is that
<( s.d. of operator A)^2> <( s.d. of operator B)^2> >= 1/4 |<[A,B]>|^2 + 1/4 |<{s.d of A, s.d of B}>|^2

I hope it is not difficult to read, as I don't know how to type it formally.
I would like to ask why the inequality finally omitted the second (the anticommutator) term ?
Sakurai said it is because the second term can only make the inequality relation stronger.
I can't understand. Besides, I am a UG Year 1 students, but familiar to Dirac Notation as I am doing UG research on Quantum Information Theory. I hope anyone can explain it in a easy way ^^ Thank You

 

[nicksauce]

The second term is always positive. Therefore if LHS >= First + Second, LHS >= First will always be true. And omitting the second term makes the uncertainty principle look "nicer".

 

[tiny-tim]

Hi ChrisLM!

oooh, nicksauce has beat me to it!

anyway, have a geq: ≥, and try using the X² tag just above the Reply box )