The most general Dirac Hamiltonians in \((1+1)\) dimensions are revisited under the requirement to exhibit a supersymmetric structure. It is found that supersymmetry allows either for a scalar or a pseudo-scalar potential. Their spectral properties are shown to be represented by those of the associated non-relativistic Witten model. The general discussion is extended to include the corresponding relativistic and non-relativistic resolvents. As example, the well-studied relativistic Dirac oscillator is considered and the associated resolved kernel is found in a closed-form expression by utilising the energy-dependent Green’s function of the non-relativistic harmonic oscillator. The supersymmetric quasi-classical approximation for the Witten model is extended to the associated relativistic model.

在（）（1 + 1）\）维度上最普通的狄拉克哈密顿量被重新提出以展现超对称结构。发现超对称性允许标量或伪标量电势。它们的光谱特性显示为由相关的非相对论Witten模型的光谱特性表示。一般讨论扩展到包括相应的相对论者和非相对论者。例如，考虑充分研究的相对论狄拉克振荡器，并通过利用非相对论谐波振荡器的依赖于能量的格林函数，以闭式形式找到相关的解析核。Witten模型的超对称准经典近似被扩展为相关的相对论模型。