This paper revisits the quantum mechanics for one photon from the modern
viewpoint and by the geometrical method. Especially, besides the ordinary
(rectangular) momentum representation, we provide an explicit derivation for
the other two important representations, called the cylindrically symmetrical
representation and the spherically symmetrical representation, respectively.
These other two representations are relevant to some current photon experiments
in quantum optics. In addition, the latter is useful for us to extract the
information on the quantized black holes. The framework and approach presented
here are also applicable to other particles with arbitrary mass and spin, such
as the particle with spin 1/2.