{"knowledge_schema": {"broad_category": "Quantum Mechanics \u2192 Many-Particle Systems \u2192 Energy Levels", "refinement": "This problem involves calculating the total energy of a system of identical spin-1/2 particles in a quantum mechanical potential well, considering the Pauli exclusion principle and the allowed quantum states.", "specific_scope": "The focus is on a one-dimensional infinite potential well where four spin-1/2 particles occupy the lowest energy states, specifically three in the ground state (n=1) and one in the first excited state (n=2).", "goal": "Calculate the total energy of the system for the ground state configuration of the particles."}, "summary": "In this quantum mechanics problem, we are tasked with finding the total energy of four identical spin-1/2 particles in a one-dimensional infinite potential well. The ground state configuration has three particles in the n=1 state and one particle in the n=2 state. The energy levels are quantized, and we use the formula E = \u03c0\u00b2\u0127\u00b2/2mL\u00b2 to express the energies. By calculating the contributions from each particle's state, we find that the total energy for the ground state is 7E."}