The Wave Function of the Lyman-Alpha Photon Part II. The Shape, Position, and Trajectory of the Photon

Abstract

In Part I of the present paper we derived the wave function of the Lyman- $ \alpha $ photon in both the linear and angular momentum bases using relativistic concepts for the photon wave function. In the present paper, Part II, we derive two $ \vec{X} $ -representations. In the first we assume one-particle theory for the photon wave function and the usual commutation rules for the position operators $ X_i $ and linear momentum operators $ P_i $ . The second representation employs the quantized photon field to derive an $ \vec{X} $ -representation. The stress, energy tensor density is used to provide a probability density in $ \vec{x} $ -space which is relativistic. The two methods of defining $ \vec{x} $ -space are compared.¶It is found in the present case that, despite the use of particle operators, the photon resembles a field far more than it does a particle.