Can someone prove the uncertainty principle for me

[Maurice7510]

My qm textbook, aptly named "quantum mechanics", is by McIntyre, though it omits the proof for the uncertainty principle and simply states it as ∆A∆B ≥ 1/2|〈[A,B]〉|. In words, if that's unclear, this is 'the product of the rms deviations of A and B is greater than/equal to one half the absolute value of the mean of the commutator of A and B. It says to look elsewhere for the proof, and normally I wouldn't be bothered, but since this leads to Heisenberg's highly unintuitive result, ∆x∆p ≥ h/4π, i feel like a proof is very necessary. If anyone could prove this for me, I'd be very greatful

 

[strangerep]

It's a consequence of the commutation relations. Ballentine covers it in section 8.4.

 

[Maurice7510]

who's ballentine?

 

[Cthugha]

Ballentine is the author of a quite popular book on quantum mechanics. As all the people writing books on quantum mechanics tend to call their books, "quantum mechanics", too, it has become quite usual to just name the author instead of the title of the book as "the book Quantum Mechanics covers it in section 8.4." would not really be a helpful information.

In this case, the exact name of the book is "Quantum Mechanics -- A Modern Development".

 

[ZapperZ]

http://www.tjhsst.edu/~2011akessler/notes/hup.pdf
http://onlinelibrary.wiley.com/doi/10.1002/9781118148419.app1/pdf

Zz.