{"knowledge_schema": {"broad_category": "Quantum Mechanics \u2192 Observables \u2192 Expectation Values", "refinement": "This problem involves calculating the expectation value of an observable represented by a matrix for a given quantum state represented by a state vector.", "specific_scope": "The task is to compute the expectation value \u27e8Q\u27e9 = \u27e8\u03c8|Q|\u03c8\u27e9 using the provided state vector and observable matrix.", "goal": "Determine the expectation value of the observable Q for the quantum state |\u03c8\u27e9."}, "summary": "In this quantum mechanics problem, we need to calculate the expectation value of an observable represented by a matrix for a specific quantum state. The expectation value is computed using the formula \u27e8Q\u27e9 = \u27e8\u03c8|Q|\u03c8\u27e9, where |\u03c8\u27e9 is the state vector and Q is the observable matrix. By performing the necessary matrix operations, we find that the expectation value is 0, indicating that the average measurement outcome of the observable in this state is zero."}