We study the Massless Semi-Relativistic Harmonic Oscillator within the framework of quantum mechanics with a Generalized Uncertainty Principle (GUP). The latter derives from the idea of minimal observable length, a quantity whose existence is expected to affect the energy eigenvalues and the eigenfunctions of the system. These effects are worked out, to the first order in the deformation parameter, using a perturbative approach based on Brau’s representation of position and momentum operators. Besides, we have discussed the impact of the GUP on the known duality between the considered model and the Schrodinger equation with a linear potential.

中文翻译：

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广义不确定性原理和半相对论谐波振荡器

我们在具有广义不确定性原理 (GUP) 的量子力学框架内研究了无质量半相对论谐波振荡器。后者源自最小可观察长度的概念，该量的存在预计会影响系统的能量特征值和特征函数。使用基于 Brau 的位置和动量算子表示的微扰方法，将这些影响计算为变形参数的一阶。此外，我们还讨论了 GUP 对所考虑模型和具有线性势的薛定谔方程之间已知对偶性的影响。