{"knowledge_schema": {"broad_category": "Physics \u2192 Quantum Mechanics \u2192 Energy Spectrum of Quantum Systems", "refinement": "This problem involves analyzing the energy levels of a quantum mechanical particle in a specific potential that depends on spherical coordinates.", "specific_scope": "The focus is on determining the energy spectrum of a particle in a potential that combines harmonic and angular components, specifically in three-dimensional space.", "goal": "To derive the energy levels of the quantum system based on the given potential and identify the correct expression for the energy spectrum."}, "summary": "This problem pertains to quantum mechanics, specifically the energy spectrum of a particle in a potential defined in spherical coordinates. The potential combines a harmonic term and an angular term, leading to a specific form of the energy levels. The task is to analyze the potential and derive the energy spectrum, ultimately identifying the correct expression from the provided candidates. The correct answer is E = (2n_x + n_y + n_z + 3/2)\u210f\u221a(k/m), which reflects the contributions from the different dimensions of motion."}