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arXiv · 1105.4512

The unified quantum wave equation

Arbab I. Arbab
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Abstract

The quaterionic formulation of quantum mechanics yields the unified quantum wave equation (UQWEs). From these equations, Dirac, Klein - Gordon and Schrodinger equations can be derived. While the UQWEs represent a matter wave (de Broglie), the Maxwell equations represent a transverse wave (field). Owing to UQWEs, the spin-0 and spin-1/2 particle are described by a wavepacket consisting of waves traveling to the left and to the right with speed of light. UQWEs show that spin-0 and spin-1/2 are in continuous states of creation and annihilation that are compatible with Heisenberg uncertainty relation. The creation - annihilation process is a result of the time translation property of the particle wavefunction. These are $E'=E-im_0c^2$ and $E'=E\pm m_0c^2$, for Klein-Gordon' and Dirac' particles, respectively. It is found that $\frac{\hbar}{m_0c^2}$ is the period of the creation -annihilation process.

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Arbab I. Arbab. 2011-05-14. The unified quantum wave equation. https://arxiv.org/abs/1105.4512

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