{"knowledge_schema": {"broad_category": "Physics \u2192 Quantum Mechanics \u2192 Energy Spectrum of Particles", "refinement": "This problem involves analyzing the energy levels of a quantum mechanical particle in a two-dimensional potential field defined by a specific mathematical function.", "specific_scope": "The focus is on determining the energy spectrum of a particle with mass m in a potential V(r, \u03b8) that combines harmonic and angular components.", "goal": "To derive the expression for the energy levels of the particle based on the given potential and identify the correct formula from the provided candidates."}, "summary": "This problem is rooted in quantum mechanics, specifically in finding the energy spectrum of a particle in a two-dimensional potential. The potential function combines a harmonic term and an angular term, leading to a specific form of energy levels. The task is to derive the energy expression based on the potential and select the correct formula from the given options. The correct answer is E = (3n_x+n_y+2)\u210f\u221a(k/m), which reflects the quantized energy levels of the system."}