  In this paper, we introduce the Schrodinger equation with a general kinetic
energy operator. The conservation law is proved and the probability continuity
equation is deducted in a general sense. Examples with a Hermitian kinetic
energy operator include the standard Schrodinger equation, the relativistic
Schrodinger equation, the fractional Schrodinger equation, the Dirac equation,
and the deformed Schrodinger equation. We reveal that the Klein-Gordon equation
has a hidden non-Hermitian kinetic energy operator. The probability continuity
equation with sources indicates that there exists a different way of
probability transportation, which is probability teleportation. An average
formula is deducted from the relativistic Schrodinger equation, the Dirac
equation, and the K-G equation.
