How Many Base States Should Incompatible Observable B Have?

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Homework Help Overview

The discussion revolves around the relationship between two incompatible observables, A and B, in quantum mechanics, specifically focusing on the number of base states that observable B should possess given that observable A has four base states.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the idea that the number of base states for observable B might be the same as for A, while others question whether B's states could be a subspace of A's basis states. There is also a consideration of how states 3 and 4 from A might need representation in B.

Discussion Status

The discussion includes varying perspectives on the relationship between the base states of A and B, with some participants expressing agreement and others providing alternative viewpoints. There is an ongoing exploration of how the states might be represented and the implications of compatibility.

Contextual Notes

Participants are considering the implications of Heisenberg's uncertainty principle and the nature of incompatible observables in their reasoning.

giants86
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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.
 
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I agree with that.
 
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)?
 
State 3 and 4 need some representation in B, too.
(1',2') can be rotated (1,2).
 
You are right, thanks
 

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