Photon position eigenvectors lead to complete photon wave mechanics

Margaret Hawton

doi:10.1117/12.730703

31 August 2007 Photon position eigenvectors lead to complete photon wave mechanics

Margaret Hawton

Proceedings Volume 6664, The Nature of Light: What Are Photons?; 666408 (2007) https://doi.org/10.1117/12.730703
Event: Optical Engineering + Applications, 2007, San Diego, California, United States

Abstract

We have recently constructed a photon position operator with commuting components. This was long thought to be impossible, but our position eigenvectors have a vortex structure like twisted light. Thus they are not spherically symmetric and the position operator does not transform as a vector, so that previous non-existence arguments do not apply. We find two classes of position eigenvectors and obtain photon wave functions by projection onto the bases of position eigenkets that they define, following the usual rules of quantum mechanics. The hermitian position operator, r⁁⁽⁰⁾, leads to a Landau-Peierls wave function, while field-like eigenvectors of the nonhermitian position operator and its adjoint lead to a biorthonormal basis. These two bases are equivalent in the sense that they are related by a similarity transformation. The eigenvectors of the nonhermitian operators r⁁^(±½) lead to a field-potential wave function pair. These field-like positive frequency wave functions satisfy Maxwell's equations, and thus justify the supposition that MEs describe single photon wave mechanics. The expectation value of the number operator is photon density with undetected photons integrated over, consistent with Feynman's conclusion that the density of non-interacting particles can be interpreted as probability density.

Citation Download Citation

Margaret Hawton "Photon position eigenvectors lead to complete photon wave mechanics", Proc. SPIE 6664, The Nature of Light: What Are Photons?, 666408 (31 August 2007); https://doi.org/10.1117/12.730703

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available