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What is the problem if we try to interpret KG equation as a single particle equation? Also I wish to know whether the born interpretation of wavefunction is applicable in relativistic quantum mechanics.

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There is no part of the physics involved that requires particle number to be conserved. Combine this with E=mc^2, which allows for energy to be converted into particle-antiparticle pairs, even when there is not enough energy to create such a pair, virtual particles allow for the temporary appearance of particles in a system that doesn't have sufficient energy for them. As such we cannot treat relativistic quantum equations as being based on particles, instead we treat them as fields with a certain energy, and assume the particle number of this field to not be constant.

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True. But still the Dirac equation for expamle has great use when dealing with single particles. Corrections to the Schroedinger equations can be derived from it and at times an application might even call for the full Dirac equation to be solved. The Klein-Gordon-Equation is much less useful when dealing with single particles. – Neuneck Feb 2 '14 at 21:26

If you try to construct the probablilty current for the KG equation, its zero component $j^0$ is not positive definite, even though you want to interpret it as a probability.

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