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Question: consider a system with the hamiltonian h for this system...

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Consider a system with the Hamiltonian, H. For this system, A is an operator. They can be described by the following matrices, where e has units of energy: -10 H=e(-1 1 0 0 4 0 0 1 0/The basis set for these operators are the unit vectors, and all states can be written as a sum of these basis vectors. However, Hand A are not diagonal in this basis (we should find arn appropriate basis set -the eigenstates-for each. (a) If we measured energy from a random initial state, what possible values could we obtain? (b) Suppose we took a measurement of the energy, and got the result: -s. Immediately afterwards, we measure the observable corresponding to the operator A. What possible values could we obtain from this measurement, and what are the probabilities of measuring each possible value? (c) After this measurement, what are the possible states we can exist in? Are these states orthogonal to each other? (d) Calculate the expectation value, (A), for this second measurement, and the associated uncertainty, ΔΑ.

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