{"knowledge_schema": {"broad_category": "Physics \u2192 Quantum Mechanics \u2192 Wave Functions", "refinement": "This problem involves understanding the properties of wave functions and their normalization in quantum mechanics.", "specific_scope": "The focus is on determining the normalization constant 'a' for a given wave function of a particle confined to a specific region of space (between x=1 and x=3).", "goal": "Calculate the value of 'a' such that the wave function is properly normalized over the specified interval."}, "summary": "This problem is rooted in quantum mechanics, specifically in the normalization of wave functions. The wave function provided describes the behavior of a particle in a confined space, and the goal is to find the normalization constant 'a' that ensures the total probability of finding the particle within the specified range (between x=1 and x=3) equals 1. This involves integrating the square of the wave function over the given interval and solving for 'a'."}