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General State Vector & Successive Measurements

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Question: Give a property that an operator A must have if it represents the physical quantity A of a system described by quantum mechanics. Two such operators A and B represent the quantities A and B of a system. A and B commute. The states |a, b>, where a = 1, 2, 3 and b = 6, 7 are a complete set of simultaneous eigenstates of A and B, and ah and bh^2 are the corresponding eigenvalues. Write down the most general state vector which describes the quantities A and B for the system.

The system is in the state

|psi> = 1/(square root 6) |1, 6> 2 / (square root 6) |2, 7> + 1 / (square root 6) |3, 7>.

What values could result from successive measurements of A then B and what would their probabilities be? Explain whether or not the results would be different if the order of measurement were reversed.

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Solution Summary

General state vectors and successive measurements are used to describe two quantities, A and B, for a system.

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