{"knowledge_schema": {"broad_category": "Physics \u2192 Quantum Mechanics \u2192 Particle in a Box", "refinement": "This problem involves calculating the energy levels of a quantum particle confined in a one-dimensional potential well, specifically using the particle in a box model.", "specific_scope": "The focus is on determining the energy difference between two specific quantum states (n=1 and n=3) of an electron in a one-dimensional box of length L.", "goal": "Calculate the energy difference between the n=1 and n=3 states using the formula for energy levels in a particle in a box."}, "summary": "This problem is rooted in quantum mechanics, specifically the particle in a box model, which describes the quantized energy levels of a particle confined in a one-dimensional space. The task is to calculate the energy difference between the first (n=1) and third (n=3) quantum states of an electron. By applying the formula for energy levels in a one-dimensional box, we can find the energy difference, which is given as 1.5 x 10^-18 J."}