{"knowledge_schema": {"broad_category": "Physics \u2192 Quantum Mechanics \u2192 Energy Levels in Potential Systems", "refinement": "This problem involves analyzing a quantum mechanical system with a specific potential energy function in two dimensions.", "specific_scope": "The focus is on determining the energy levels of a particle in a two-dimensional potential defined by a quadratic term and an angular-dependent term.", "goal": "Identify the correct expression for the energy levels of the system based on the given potential."}, "summary": "In this problem, we are tasked with finding the energy levels of a quantum particle in a two-dimensional space with a specific potential energy function. The potential consists of a harmonic term and an angular-dependent term, which influences the quantization of energy levels. The goal is to derive the correct expression for the energy levels from the provided candidates, leading to the conclusion that the energy levels are given by E = (2n_x+n_y+3/2)\u210f\u221a(k/m). This highlights the importance of understanding the relationship between potential energy and quantized states in quantum mechanics."}