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Quaternionic quantum harmonic oscillator

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Abstract

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.

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Authors and Affiliations

  1. Departamento de Matemática Pura e Aplicada, Universidade Federal do Rio Grande do Sul (UFRGS), Avenida Bento Gonçalves 9500, Caixa Postal 15080, 91501-970, Porto Alegre, RS, Brazil

    Sergio Giardino

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  1. Sergio Giardino
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Correspondence to Sergio Giardino.

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Giardino, S. Quaternionic quantum harmonic oscillator. Eur. Phys. J. Plus 136, 120 (2021). https://doi.org/10.1140/epjp/s13360-021-01103-w

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