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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.16602 |
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Table of Contents:
- Within this article one finds the statement of the Klein-Gordon problem within the real Hilbert space formalism ($\mathbbm R$HS) in terms of complex wave functions, and in terms of quaternionic wave functions as well. The complex formulation comprises hermitian and non-hermitian cases, while the quaternionic solutions additionally set in motion self-interacting particles. The non-hermitian cases comprise non-conservative processes, while the self-interaction physically implies the increase of the effective mass of the particle, an effect that cannot be reproduced using a complex wave function. The obtained autonomous particle solutions, as well as the Klein problem agree to the previously discovered self-interacting non-relativistic particle, and thus reinforce $\mathbbm R$HS as viable and consistent way to explore open problems in quantum mechanics. Also important, the negative energy problem that plagues the usual formalism is eliminated within this approach.