{"knowledge_schema": {"broad_category": "Physics \u2192 Quantum Mechanics \u2192 Wave Functions", "refinement": "This problem involves normalizing a wave function, which is a fundamental concept in quantum mechanics that ensures the total probability of finding a particle in a given space is equal to one.", "specific_scope": "The focus is on a specific wave function defined for particles in a one-dimensional space, constrained between two points (x=1 and x=3), and determining the normalization constant 'b'.", "goal": "Calculate the value of 'b' that makes the integral of the absolute square of the wave function over the specified range equal to one."}, "summary": "This problem is rooted in quantum mechanics, specifically in the normalization of a wave function. The wave function provided describes the state of particles moving in a tube, and the task is to find the normalization constant 'b' such that the total probability of finding a particle between x=1 and x=3 equals one. This involves integrating the absolute square of the wave function over the specified range and solving for 'b'. The correct answer is 0.85."}