{"knowledge_schema": {"broad_category": "Quantum Mechanics \u2192 Wave Functions \u2192 Probability Density", "refinement": "This problem involves understanding the properties of wave functions and how they relate to the probability of finding particles in a given region of space.", "specific_scope": "The focus is on determining the normalization constant (b) in the wave function of a particle, given the constraints of its position measurements.", "goal": "Calculate the value of the normalization constant (b) such that the probability of finding the particle between x=2 and x=4 is equal to 1."}, "summary": "This problem is rooted in quantum mechanics, specifically in the context of wave functions and probability densities. It requires calculating the normalization constant (b) for a given wave function, ensuring that the total probability of finding a particle within a specified range (between x=2 and x=4) equals 1. The solution involves integrating the probability density derived from the wave function and solving for b, leading to the conclusion that the value of b is 0.72."}