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Question: consider the following operators for a twolevel quantum system where...

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Consider the following operators for a two-level quantum system, where α+ and | alpha _{-} angle are normalized eigenvectors of hat alpha...

hat{alpha } equiv rac{1}{2} (|alpha _{+} angle langle alpha _{+}| - |alpha _{-} angle langlealpha _{-}|)

hat{eta } equiv rac{1}{2} (|alpha _{+} angle langle alpha _{-}| + |alpha _{-} angle langlealpha _{+}|)

hat{gamma } equiv rac{1}{2} (-i|alpha _{+} angle langle alpha _{-}| + i |alpha _{-} angle langlealpha _{+}|)

Determine an expression for the commutator [hat eta ,hat gamma ] and express this in terms of hat alpha. What does this tell us about the uncertainty in simultaneous measurements of the physical quantities, eta and gamma, both for a general state (in terms of an expectation value), and specifically for the state |alpha _{+} angle .

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