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.
Conference Committee Involvement (3)
The Nature of Light: What are Photons? IV
22 August 2011 | San Diego, California, United States
The Nature of Light: What are Photons? III
3 August 2009 | San Diego, California, United States
The Nature of Light: What are photons?
26 August 2007 | San Diego, California, United States
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
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.