Abstract
A series of novel state-vector functions (SVFs), which is the general solution of the Schrödinger equation for a photon, are constructed. Each set of these functions consists of a triplet of eigen-SVFs: The triplet can be broken down into a pair of nonzero l-order functions and a single zero-order function. The photons, described with a triplet of eigen-SVFs, possess all the quantum characteristics of a photon: In addition to common attributes like energy E = ħ ω , and momentum p z = ħ κ , they also exhibit different angular momenta (AM) L z+ = lħ, L z− = lħ, and L z0 = 0, where l⩾1. In other words, in addition to usual eigenvalues L z±= ±ħ, there are unusual nonzero l-order eigenvalues L z± = ±lħ and a zero-order eigenvalue L z0 = 0 for AM of a photon. By a series of SVFs, the pattern from nonzero l-order and zero-order Laguerre-Gaussian modes of a laser beam is explained well from a quantum mechanical point of view.
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Yao, Z., Zhong, J., Mao, B. et al. Extraordinary photons with unusual angular momentum. Sci. China Ser. G-Phys. Mech. Astron. 52, 166–176 (2009). https://doi.org/10.1007/s11433-009-0031-3
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DOI: https://doi.org/10.1007/s11433-009-0031-3