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arXiv · 1802.04266

Probability density of relativistic spinless particles

M. J. Kazemi·H. Hashamipour·M. H. Barati
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Abstract

In this paper, a new conserved current for Klein-Gordon equation is derived. It is shown, for $1+1$-dimensions, the first component of this current is non-negative and reduces to $|\phi|^2$ in non-relativistic limit. Therefore, it can be interpreted as the probability density of spinless particles. In addition, main issues pertaining to localization in relativistic quantum theory are discussed, with a demonstration on how this definition of probability density can overcome such obstacles. Our numerical study indicates that the probability density deviates significantly from $|\phi|^2$ only when the uncertainty in momentum is greater than $m_0c$.

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M. J. Kazemi, H. Hashamipour, M. H. Barati. 2018-02-12. Probability density of relativistic spinless particles. https://doi.org/10.1103/physreva.98.012125

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