Uncertainty Operators in Nouredine Zettili's Book

[Seanskahn]

Hello community.

My second stupid question.

In the book by Nouredine Zettili , the uncertaintie operators are defined as $$\Delta$$A = A - <A>, where A is an operator, and <A> = <$$\psi$$|A|$$\psi$$> , with repect to a normalized state vector |$$\psi$$>

i was wondering, why is not the uncertainty defined as: A ~ <A>, i.e., the ~ (difference operator) in place of the - (substraction operator)

 

[sweet springs]

Hi, sean_s.

i was wondering, why is not the uncertainty defined as: A ~ <A>, i.e., the ~ (difference operator) in place of the - (substraction operator)

What is 'difference operator' ? What is the definition?
Regards.

 

[Seanskahn]

What is 'difference operator' ? What is the definition?
Regards.

difference opearator is simply as follows:

(a~b) = |a-b| , i.e. the absolute difference.

 

[nnnm4]

That definition says that the expectation value for the "uncertainty" for an arbitrary state is zero

DeltaA = A - <A> --->

<DeltaA> = <psi| A |psi > - <A><psi|psi>
= <A> - <A> = 0

 

[nnnm4]

By the way do you have a reference for the definition of the "difference operator"?

 

[Seanskahn]

DeltaA = A - <A> --->

<DeltaA> = <psi| A |psi > - <A><psi|psi>
= <A> - <A> = 0

thats right
the expectation value of $$\Delta$$A (which you write by <DeltaA>) IS zero ... remember expection value of the uncertainty is NOT the uncertainty.

the difference operator i learned in the elementary school

 

[dextercioby]

There's only one operator in a Hilbert space (and thus in the QM mathematical formalism): the difference of 2 arbitrary operators (as opposed to the sum of 2 operators). You denote this operation by the sign "-" called "minus".

 

[nickthrop101]

this may seem a stupid question. but in an equation, wat does the delta sign mean?

 

[Fredrik]

In this context, nothing. $\Delta A$ should be interpreted as a single symbol.

 

[Seanskahn]

bigubau... THANKS! - I am sooo stupid, i did not notice that part

all others, thanks for the contributions