Quantum mechanics
Maths and statistics discussion, revision, exam and homework help.
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Quantum mechanics
are two Hermitian operators. consider the state 
where 
is real and 
. By taking the inner products on both sides and minimizing with respect to derive the uncertainty relation:
![\Delta A^2 \Delta B^2 \geq \frac{1}{4} (i \langle [A,B] \rangle)^2](http://www.thestudentroom.co.uk/latexrender/pictures/94/944ece8d9a0ef61016c59a237e72583b.png "\Delta A^2 \Delta B^2 \geq \frac{1}{4} (i \langle [A,B] \rangle)^2")
where ![[\hat{A}, \hat{B}] = \hat{A} \hat{B} - \hat{B} \hat{A}](http://www.thestudentroom.co.uk/latexrender/pictures/96/963f089c35609c330c8918461d7e1f30.png "[\hat{A}, \hat{B}] = \hat{A} \hat{B} - \hat{B} \hat{A}")
is the commutator of 
with 
and 
I've been stuck on this question for a while and would appreciate any help. Thanks. -
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Re: Quantum mechanicsWhat's lower case delta?(Original post by JBKProductions)
are two Hermitian operators. consider the state where is real and . By taking the inner products on both sides and minimizing with respect to derive the uncertainty relation:
where is the commutator of with and
I've been stuck on this question for a while and would appreciate any help. Thanks. -
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Re: Quantum mechanicsThe lower case delta is(Original post by ben-smith)
What's lower case delta?
. Where 
and 
Last edited by JBKProductions; 10-04-2012 at 10:57.
