How Many Base States Should Incompatible Observable B Have?

[giants86]

Homework Statement

Say I have two incompatible observables A and B. A has a finite number of base states say 4. How many base states should B have?

Homework Equations

Heisenberg's uncertainty

AB - BA <> 0

The Attempt at a Solution

I guess the answer is 4 as A and B basis states should form basis in the same space, but not very sure.

 

[mfb]

I agree with that.

 

[giants86]

have a second thought. If A's states are (1), (2), (3), (4), can't B states be a subspace of that basis, such as (1') = 1/sqrt(2) [(1) + (2)]; (2') = 1/sqrt(2) [(1)- (2)], no contribution from (3) and (4)?

 

[mfb]

State 3 and 4 need some representation in B, too.
(1',2') can be rotated (1,2).

 

[giants86]

You are right, thanks