{"knowledge_schema": {"broad_category": "Quantum Mechanics \u2192 Atomic Physics \u2192 Hydrogen Atom", "refinement": "This problem involves understanding the selection rules for dipole transitions between quantum states of the hydrogen atom.", "specific_scope": "The focus is on identifying the correct transition path between specific quantum states and calculating the associated probability of that transition.", "goal": "Determine the correct sequence of dipole transitions from the state |3,0,0\u27e9 to |1,0,0\u27e9 and the probability of that transition."}, "summary": "In this problem, we analyze the dipole transitions between quantum states of a hydrogen atom. The task is to identify the correct transition path from the state |3,0,0\u27e9 to |1,0,0\u27e9 and to calculate the probability of that transition. The correct path is |3,0,0\u27e9\u2192|2,1,0\u27e9\u2192|1,0,0\u27e9 with a probability of 1/3, which adheres to the selection rules governing allowed transitions in quantum mechanics."}