In classical mechanics, the negative energy solutions can be dismissed as being
unphysical. However, in quantum mechanics all solutions are required to form a
complete set of states, and the negative energy solutions simply cannot be dis-
carded. Whilst it is not clear how the negative energy solutions should be inter-
preted, there is a more serious problem with the associated probability densities.
The expressions for the probability density and probability current for the Klein–
Gordon equation can be identified following the procedure used in Section 2.3.2.
Taking the difference ∗
× (4.1) − × (4.1)
∗
gives