{"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 normalization of wave functions for identical particles confined to a specific region. The wave function provided must be normalized over the interval from x=1 to x=3, which means that the integral of the absolute square of the wave function over this range must equal 1. The task is to find the appropriate value of the constant 'a' from the given candidates that satisfies this normalization condition."}