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Formulation and picture of quantum phase

Science China(Physics,Mechanics & Astronomy) 2009年第12期52卷 1949-1960页

作者： YAO ZhiXin ZHONG JianWei PAN BaiLiang Department of Physics Zhejiang UniversityHangzhou 310027China School of Sciences Hangzhou Dianzi UniversityHangzhou 310018China

Based on the concept of classical phase,we formulate a new explanation for the quantum phase from the quantum mechanical point of view. The quantum phase is the canonically conjugate variable of an angular momentum operator,which corresponds to the angular position θ in an actual physical space with a classical reference frame,but it takes a complex exponential form eiθ≡cosθ +i sinθ in the abstract Hilbert space of a quantum reference frame. This formulation is simply the famous Euler formula in a complex number field. In particular,when θ = π/2,the correlative quantum phase is a unitary pure imaginary number eiπ/2 ≡cos(π/2)+i sin(π/2) ≡ i. By using a photon state-vector function that is the general solution of photon Schrdinger equation and can completely describe a photon's behavior,we discuss the relationship between the angular momentum of a photon and the phase of the photon; we also analyze the intrinsic relationship between the macroscopic light wave phase and the microscopic photon phase.

关键词： formulation quantum phase photon state-vector function polarization

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Extraordinary photons with unusual angular momentum

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Science China(Physics,Mechanics & Astronomy) 2009年第2期52卷 166-176页

作者： YAO ZhiXin ZHONG JianWei MAO BangNing PAN BaiLiang Department of Physics Zhejiang UniversityHangzhou 310027China

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.

关键词： photon photon equation state-vector function photon angular momentum laser mode

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