摘要
A series of novel state-vector functions (SVFs), which is the general solution of the Schr?dinger 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 = ? ω , and momentum p z = ? κ , they also exhibit different angular momenta (AM) L z+ = l?, L z? = l?, and L z0 = 0, where l?1. In other words, in addition to usual eigenvalues L z±= ±?, there are unusual nonzero l-order eigenvalues L z± = ±l? 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.
A series of novel state-vector functions (SVFs), which is the general solution of the Schrdinger equa- tion 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 = hω, and momentum pz = hκ, they also exhibit different angular momenta (AM) Lz+ = lh, Lz- = lh, and Lz0 = 0, where l≥1. In other words, in addition to usual ei- genvalues Lz±= ±h, there are unusual nonzero l-order eigenvalues Lz±= ±lh and a zero-order eigenvalue Lz0 = 0 for AM of a photon. By a series of SVFs, the pattern from nonzero l-order and zero-order La- guerre-Gaussian modes of a laser beam is explained well from a quantum mechanical point of view.
