On The Probability Density of Spinless Particles.
In this paper, we shall derive a new conserved current for Klein-Gordon equation. The first component of this current is non-negative and reduces to $|\phi|^2$ in the non-relativistic limit. Therefore, it can be interpreted as a suitable probability density for spinless particles. In addition, this current is time-like and so prevents faster than light particle propagation. We will see the probability density has a considerable deviation from $|\phi|^2$ providing the uncertainty in momentum is much greater than $m_0c$.
Publisher URL: http://arxiv.org/abs/1802.04266
DOI: arXiv:1802.04266v1
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