{"knowledge_schema": {"broad_category": "Quantum Mechanics \u2192 Operators and Uncertainty", "refinement": "This problem involves calculating the uncertainty of an observable (Q_z) when the system is in a specific eigenstate of another observable (Q_x).", "specific_scope": "The focus is on determining the uncertainty in the measurement of the operator Q_z given the state of the system represented by a specific eigenvector of Q_x.", "goal": "Calculate the uncertainty \u0394 Q_z of the operator Q_z based on the provided eigenstate and its relation to the operators Q_x and Q_z."}, "summary": "In this quantum mechanics problem, we are tasked with finding the uncertainty \u0394 Q_z of the operator Q_z when the system is in an eigenstate of the operator Q_x. The eigenstate is given as a specific column vector, and we need to use the properties of the operators and their matrix representations to compute the uncertainty. The answer to the uncertainty \u0394 Q_z is \u0127/\u221a(2), indicating the spread in the possible measurement outcomes of the observable Q_z when the system is in the specified state."}