{"knowledge_schema": {"broad_category": "Physics \u2192 Quantum Mechanics \u2192 Wave Functions", "refinement": "This problem involves understanding the properties of wave functions and normalization in quantum mechanics, particularly for identical particles in a confined space.", "specific_scope": "The focus is on determining the normalization constant 'a' for the given wave function of particles confined between specific boundaries (x=1 and x=3).", "goal": "Calculate the value of 'a' such that the wave function is properly normalized over the specified range."}, "summary": "This problem is rooted in quantum mechanics, specifically in the context of wave functions and their normalization. The wave function provided describes the behavior of identical particles confined to a specific region (between x=1 and x=3). To find the numerical value of 'a', we need to ensure that the wave function is normalized, meaning the integral of the absolute square of the wave function over the defined range equals 1. The task involves applying the normalization condition to determine the correct value of 'a' from the given candidates."}