{"knowledge_schema": {"broad_category": "Quantum Mechanics \u2192 Particle in a Box \u2192 Energy Levels", "refinement": "This problem involves calculating the energy levels of a system of identical spin-1/2 particles confined in a one-dimensional infinite potential well.", "specific_scope": "The focus is on determining the ground state and excited state energies for a system of four identical particles, taking into account their indistinguishability and the Pauli exclusion principle.", "goal": "Calculate the energies of the ground state, first excited state, and second excited state of the system in terms of a given energy E."}, "summary": "This problem is rooted in quantum mechanics, specifically the behavior of particles in a one-dimensional infinite potential well. It requires calculating the energy levels for a system of four identical spin-1/2 particles, considering their indistinguishability and the Pauli exclusion principle. The goal is to find the energies of the ground state, first excited state, and second excited state, which are given as multiples of a defined energy E. The correct answer is 10E, 15E, and 18E."}