Quaternionic Quantum Particles: New Solutions

TL;DR: Researchers generalize quaternionic quantum mechanics to add angular momenta and circular potential, obtaining quaternionic solutions in terms of Bessel functions, extending complex number applications in quantum mechanics to non-commutative quaternions with four components.

TL;DR: In this paper, the Klein-Gordon equation was solved in the framework of real Hilbert space approach to quaternionic quantum mechanics, which is the simplest known solution for quaternion quantum theories and the closest to the complex solution.

TL;DR: In this paper, the quaternionic Dirac equation was solved in the real Hilbert space, and the free particle solutions set was shown to be eight elements in the case of a massive particle, and four elements for a massless particle.

TL;DR: In this paper, the Klein-Gordon equation was solved in the framework of real Hilbert space approach to quaternionic quantum mechanics and the solution was the simplest ever obtained for quaternion quantum theories.

TL;DR: In this article, a quaternionic quantum field theory was formulated when the numbers of bosonic and fermionic degrees of freedom are equal and the fermions, as well as the bosons, obey a second order wave equation.

TL;DR: It is shown that the transmission coefficient may pick up a phase change on reversal of the barrier order, and commented on why this phase change would not necessarily be observed in experiments.

TL;DR: In this paper, the authors present a formalism for treating one-dimensional problems in quaternionic quantum mechanics, and derive an explicit form for the T matrix for scattering from a square barrier, and use this result to calculate the transmission and reflection coefficients.

TL;DR: In this paper, the authors proposed a method to solve quaternionic and complex linear second order differential equations with constant coefficients, motivated by a quaternion formulation of quantum mechanics.