{"knowledge_schema": {"broad_category": "Physics \u2192 Quantum Mechanics \u2192 Energy Spectrum of Quantum Systems", "refinement": "This problem involves analyzing a quantum mechanical particle in a two-dimensional potential that combines harmonic and angular components.", "specific_scope": "The focus is on determining the energy levels of a particle in a potential given by V(r, \u03b8) = (1/2)kr\u00b2 + (3/2)kr\u00b2cos\u00b2(\u03b8), which suggests a coupling between radial and angular motion.", "goal": "To derive the energy spectrum of the quantum mechanical system based on the given potential."}, "summary": "This problem requires understanding the energy spectrum of a quantum mechanical particle in a two-dimensional potential that combines harmonic and angular components. The potential given suggests a coupling between radial and angular motions, 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 for the energy levels from the provided candidates."}