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arXiv:1706.08370 · Canadian Journal of Physics

Quaternionic quantum particles: new solutions

Sergio Giardino

Published Apr 1, 2021• 7 citations
arXivHTMLPDF

Abstract

If Ψ is a quaternionic wave function, then iΨ ≠ Ψi. Thus, there are two versions of the quaternionic Schrödinger equation (QSE). In this article, we present the second possibility for solving the QSE, following from a previous article. After developing the general methodology, we present the quaternionic free particle solution and the scattering of the quaternionic particle through a scalar barrier.

DOI
10.1139/cjp-2020-0077

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Abstract We present two novel solutions of real Hilbert state quaternionic quantum mechanics . Firstly, we observe that the angular momentum operator admits two different classes of physically non-equivalent free particles. As a second result, we study the Larmor precession to observe that it has a quaternionic solution where a novel phenomenological interpretation is possible, as well as a different spin is possible, and these results may encourage experimental and theoretical investigations of the quaternionic theory.
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