  It is shown that the well-known relativistic correction of quantum
Hamiltonian that is present in textbooks appears after quantization of
oversimplified relativistic kinetic energy decomposition. Using the proper
expression one obtains the kinetic energy operator which relation with the
ususal one is consistent with corresponding relation of kinetic energies in
special relativity theory. The Schr\"odinger equation with this operator gives
new interesting possibilities for quantum phenomena description.
