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 |φ|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 |φ|² only when the uncertainty in momentum is greater than m₀c.