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I Distinguishable Terms in a State

  1. Apr 17, 2017 #1
    Let's say we have a proposition (or state, if we prefer) ##P\equiv \psi \equiv AB^\perp + e^{j \theta} A^\perp B## where, e.g., ##A^{\perp}## indicates some ket that is orthogonal to ##A##.

    We also have an operator ##\hat{O}## .

    Without reference to a physical context, is there a test to say whether there will be interference in the probability of observing a given eigenvalue of ##\hat{O}## as we vary the phase ##\theta## ? In other words, how would a shut-up-and-calculate robot know whether it should sum-then-square or it should square-then-sum?
     
  2. jcsd
  3. Apr 17, 2017 #2
    We need to get a projection operator ##\hat\Pi## corresponding to a given eigenvalue of ##\hat O##. Then the probability is calculated as $$ <\psi|\hat\Pi|\psi>$$ If it changes when θ changes, then we have interference.
     
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