Embedding the photon with its relativistic mass as a particle into the electromagnetic wave

Area of Science:

• Quantum optics
• Wave-particle duality
• Photonics

Background:

• The photon particle picture, based on the Schrödinger equation, successfully describes Gaussian wave probability density.
• Generalizing this model to arbitrary wave phase fronts is crucial for a comprehensive understanding of photon behavior.

Purpose of the Study:

• To extend the photon particle picture to waves with arbitrary phase front shapes.
• To derive the transverse force acting on a photon and define its transverse potential.
• To demonstrate the applicability of matter wave theory to describe photon quantum mechanical motion.

Main Methods:

• Generalization of the Schrödinger equation for photon probability density.
• Derivation of a transverse force based on relativistic mass density propagation.
• Formulation of a transverse potential for photon motion.

Main Results:

• A generalized particle picture for photons with arbitrary wave shapes.
• Derivation of a transverse force and potential governing photon motion.
• Successful application of matter wave theory to describe photon transverse quantum motion, irrespective of rest mass.

Conclusions:

• The generalized particle picture provides a unified framework for understanding photon behavior.
• The derived transverse force and potential offer new insights into photon dynamics.
• The study validates the use of matter wave theory for describing massless particles like photons.