fxdung said:The wave function of photon does not exist,but the vector state in Hilbert space still exists
Read again my post above! It exists, but it just has a different physical interpretation.fxdung said:The wave function of photon does not exist
That frequent statement is also, strictly speaking, not correct. There is a position observable for a photon, but it is not Lorentz covariant. Despite non-covariance it has a sensible physical interpretation in terms of position measurements with apparatus at rest in a specific Lorentz frame.bhobba said:That's because position is not an observable for photons hence they can't be expanded in terms of eigenfunctions of position which a wave-function is.
What interpretation? Can you give a reference?Demystifier said:Mathematically, one can introduce a wave function of a single photon, and this wave function satisfies Maxwell equations. Physically, however, such a wave function has a different interpretation than wave function in non-relativistic quantum mechanics (QM). For that reason people sometimes say that "wave function of a single photon does not exist", which really means that photon wave function with the same physical interpretation as in non-relativistic QM does not exist.
An example of a position operator in QFT, is the Newton-Wigner operator which, IIRC, its eigenvectors aren't a complete set, i.e. ## \int |x\rangle \langle x| dx \neq 1 ##, which doesn't make sense!Demystifier said:That frequent statement is also, strictly speaking, not correct. There is a position observable for a photon, but it is not Lorentz covariant. Despite non-covariance it has a sensible physical interpretation in terms of position measurements with apparatus at rest in a specific Lorentz frame.
Another correct statement is that there is no Lorentz covariant photon-position observable in the physical Hilbert space. It is possible to introduce a Lorentz covariant position observable, but in an extended Hilbert space containing non-physical states.
E.g. Fourier transform gives probability in the momentum space. For instance, Bjorken Drell 1.Shyan said:What interpretation? Can you give a reference?
I don't think it's true for the NW operator. Can you give a reference?Shyan said:Newton-Wigner operator which, IIRC, its eigenvectors aren't a complete set, i.e. ## \int |x\rangle \langle x| dx \neq 1 ##,
Sorry about that. I confused the things I read before!Demystifier said:I don't think it's true for the NW operator. Can you give a reference?
The wave function of the photon is the complex Riemann-Silberstein vector field. Unlike Schroedinger wave functions, it doesn't have a probability interpreation. But it provides a massless spin 1 representation of the Poincare group, hence has all the properties needed in quantum field theory.fxdung said:The wave function of photon does not exist,but the vector state in Hilbert space still exists.Then how does the vector state envolve in time?
A quantum equation is a mathematical formula used in quantum mechanics to describe the behavior and interactions of subatomic particles. It is used to predict the probability of a particle's state or behavior, rather than its exact position or trajectory.
A single photon is the smallest unit of light or electromagnetic radiation. It is a particle that carries energy and momentum, and it has properties of both a wave and a particle. It is also the fundamental building block of all electromagnetic radiation, including visible light, radio waves, and X-rays.
The quantum equation of a single photon is a mathematical expression that describes the wave-particle duality of a single photon. It includes variables such as the photon's energy, momentum, and position, and it is used to predict the probability of the photon's behavior in a given situation.
The quantum equation of a single photon is based on the principles of quantum mechanics, which govern the behavior of subatomic particles. Unlike classical physics equations, which describe the behavior of macroscopic objects, the quantum equation takes into account the wave-particle duality and probabilistic nature of particles at the quantum level.
Understanding the quantum equation of a single photon is important because it allows us to accurately predict and manipulate the behavior of particles at the quantum level. This is crucial for advancements in technologies such as quantum computing, cryptography, and telecommunications. It also helps us gain a deeper understanding of the fundamental nature of the universe and its building blocks.