In this article we obtained the harmonic oscillator solution for quaternionic quantum mechanics (\(\mathbb {H}\)QM) in the real Hilbert space, both in the analytic method and in the algebraic method. The quaternionic solutions have many additional possibilities if compared to complex quantum mechanics (\(\mathbb {C}\)QM), and thus there are many possible applications to these results in future research.

中文翻译：

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四元离子量子谐振子

在本文中，我们通过解析方法和代数方法获得了实际希尔伯特空间中四元数子量子力学（\（\ mathbb {H} \） QM）的谐振子解。与复杂的量子力学（\（\ mathbb {C} \） QM）相比，四元解决方案还有许多其他可能性，因此，这些结果在未来的研究中有许多可能的应用。