# The uncertainty operator and Heisenberg

1. Feb 26, 2014

### dyn

In deriving the Heisenberg uncertainty relation for 2 general Hermitian operators A and B , the uncertainty operators ΔA and ΔB are introduced defined by ΔA=A - (expectation value of A) and similarly for B.
My question is this - how can you subtract(or add) an expectation value , which is just a number to A which is an operator ?

2. Feb 26, 2014

### atyy

A number is also an operator. But you can also see it by the variance being <A.A>-<A>2, where <A.A> is a number and <A> is a number.

<(A-<A>)2>
= <A.A-2<A>A+<A>2>
= <A.A>-<2<A>A>+<<A>2>
= <A.A>-2<A><A>+<<A>2>
= <A.A>-<A>2

3. Feb 26, 2014

### WannabeNewton

There's an implicit identity operator multiplying $\langle A \rangle$.

4. Feb 27, 2014

### dextercioby

That's sloppy and indeed misleading notation. The unit operator on the states' space is not written when scaled by the expectation value.