On the Quantum Mechanics for One Photon

Abstract

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.

15 pages, typos corrected, references added, corrections and improvements made owing to the anonymous referee's responsible and helpful remarks, accepted for publication in Journal of Mathematical Physics:)

References in corpus (5)

• Entanglement of Orbital Angular Momentum States of Photons
• Bohr's Correspondence Principle and The Area Spectrum of Quantum Black Holes
• Quantum Information and Relativity Theory
• Strongly focused light beams interacting with single atoms in free space
• The Holographic Entropy Bound and Local Quantum Field Theory

Cited by in corpus (2)

• Quantum Entanglement of Electromagnetic Fields in Non-inertial Reference Frames
• On the Quantum Theory of Massless Spin-3/2 Field in Minkowski Spacetime