{"knowledge_schema": {"broad_category": "Physics \u2192 Quantum Mechanics \u2192 Energy Levels", "refinement": "This problem involves the analysis of a quantum mechanical system described by a specific potential in two dimensions, requiring the application of quantum mechanics principles to find the energy spectrum.", "specific_scope": "The focus is on a particle in a two-dimensional potential characterized by a harmonic term and an angular dependence, necessitating the use of separation of variables in polar coordinates to solve the Schr\u00f6dinger equation.", "goal": "Determine the quantized energy levels of the particle in the given potential."}, "summary": "This problem pertains to quantum mechanics, specifically the determination of energy levels for a particle in a two-dimensional potential. The potential is a combination of a harmonic term and an angular dependence, which requires solving the Schr\u00f6dinger equation using polar coordinates. The goal is to find the quantized energy spectrum, leading to the conclusion that the energy levels are given by E = (2n_x+n_y+3/2)\u210f*sqrt(k/m), where n_x and n_y are quantum numbers associated with the respective dimensions."}