{"knowledge_schema": {"broad_category": "Physics \u2192 Quantum Mechanics \u2192 Quantum Harmonic Oscillator", "refinement": "This problem involves the mathematical description of a quantum harmonic oscillator, focusing on the ground state wave function and its parameters.", "specific_scope": "The task is to determine the relationship between the constant \u03b1 in the ground state wave function and the physical parameters of the system, specifically mass (m) and angular frequency (\u03c9).", "goal": "Find the expression for \u03b1 in terms of m and \u03c9 that correctly describes the ground state wave function of the quantum harmonic oscillator."}, "summary": "This problem pertains to the quantum harmonic oscillator in quantum mechanics, where we need to relate the constant \u03b1 in the ground state wave function to the mass and angular frequency of the system. The correct expression for \u03b1 is derived from the normalization of the wave function and the properties of the harmonic oscillator, leading to the conclusion that \u03b1 = m * \u03c9 / 2\u0127. This highlights the connection between the physical parameters of the system and the mathematical formulation of its quantum state."}