{"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 find the correct expression for the energy spectrum of the quantum mechanical particle in the specified potential."}, "summary": "This problem is rooted in quantum mechanics, specifically in finding the energy spectrum of a particle in a two-dimensional potential. The potential combines a harmonic term and an angular term, indicating that the particle's motion can be separated into radial and angular components. The goal is to derive the energy levels based on the given potential and identify the correct expression from the provided candidates. The solution involves applying quantum mechanical principles to analyze the system's behavior and energy quantization."}