Quaternionic particle in a relativistic box
Sergio Giardino
TL;DR
This paper explores quaternionic solutions to the Dirac equation in a relativistic box, revealing fundamental differences from complex quantum mechanics and suggesting quaternionic quantum mechanics as a distinct framework.
Contribution
It introduces quaternionic solutions to the Dirac equation in a relativistic box, highlighting their differences from complex solutions and proposing quaternionic quantum mechanics as a potentially separate theory.
Findings
Quaternionic solutions do not reduce to complex solutions in any limit
Quaternionic quantum mechanics may describe phenomena beyond complex quantum mechanics
Potential new applications for quaternionic structures in quantum physics
Abstract
This study examines Quaternion Dirac solutions for an infinite square well. The quaternion result does not recover the complex result within a particular limit. This raises the possibility that quaternionic quantum mechanics may not be understood as a correction to complex quantum mechanics, but it may also be a structure that can be used to study phenomena that cannot be described through the framework of complex quantum mechanics.
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