关键词: 一维束缚态, 简并, 波函数节点 

Abstract: We discuss the non-degeneracy theorem for one-dimensional bound state, pointing out that the proof of this theorem in typical textbooks only applies to wave functions without zero point. For wave functions vanishing at some points, we analyze the behavior of the function near those points and prove that the theorem still holds. 

Key words: one-dimensional bound state, degeneracy, zero point of wave function