{"knowledge_schema": {"broad_category": "Quantum Mechanics \u2192 Angular Momentum", "refinement": "This problem involves the addition of angular momentum states for two identical fermions (electrons) in a p orbital state, focusing on the measurement of their z-components of angular momentum.", "specific_scope": "The task is to determine the probability of measuring both electrons in the state where their z-components of angular momentum are -\u0127, given their combined angular momentum state.", "goal": "Calculate the probability of obtaining specific eigenvalues for the z-components of angular momentum for a two-electron system."}, "summary": "In this quantum mechanics problem, we analyze the combined angular momentum state of two electrons in a p orbital. The total angular momentum state is given as |1, 1, 2, -1>, indicating that both electrons have orbital angular momentum quantum numbers of 1. When measuring the z-components of their angular momentum, we need to find the probability of both electrons having eigenvalues of -\u0127. Given the nature of the combined state and the restrictions imposed by the Pauli exclusion principle, the probability of obtaining both measurements as -\u0127 is 0."}