We propose an alternative way to introduce supersymmetric quantum mechanics to physics students using a point canonical coordinate transformation. We provide two point canonical transformations that allow us to obtain new supersymmetric partner Hamiltonians with iso-spectral and non-iso-spectral energy eigenvalues starting from a known solvable Hamiltonian. We illustrate this new approach by applying it to the harmonic oscillator potential.

中文翻译：

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通过点规范变换引入超对称量子力学

我们提出了一种使用点规范坐标变换将超对称量子力学引入物理学生的替代方法。我们提供了两点正则变换，使我们能够从已知的可解哈密顿量开始获得具有等谱和非等谱能量特征值的新超对称伙伴哈密顿量。我们通过将其应用于谐波振荡器电位来说明这种新方法。